{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T09:02:23Z","timestamp":1774947743982,"version":"3.50.1"},"reference-count":138,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T00:00:00Z","timestamp":1650931200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T00:00:00Z","timestamp":1650931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s12532-022-00221-5","type":"journal-article","created":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T15:09:31Z","timestamp":1650985771000},"page":"623-672","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Political districting to minimize cut edges"],"prefix":"10.1007","volume":"14","author":[{"given":"Hamidreza","family":"Validi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Austin","family":"Buchanan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,26]]},"reference":[{"key":"221_CR1","unstructured":"Achterberg, T.: Symmetry breaking algorithm in Gurobi. https:\/\/support.gurobi.com\/hc\/en-us\/community\/posts\/360050295511-Symmetry-Breaking-Algorithm-in-Gurobi (2020). Accessed 22 Feb 2021"},{"key":"221_CR2","doi-asserted-by":"crossref","unstructured":"Adler, W.T., Wang, S.S.H.: Response to Cho and Liu, Sampling from complicated and unknown distributions: Monte Carlo and Markov chain Monte Carlo methods for redistricting. Physica A Stat. Mech. Appl. 516, 591\u2013593 (2019)","DOI":"10.1016\/j.physa.2018.10.057"},{"issue":"3","key":"221_CR3","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1002\/net.21944","volume":"76","author":"Z Al\u00e8s","year":"2020","unstructured":"Al\u00e8s, Z., Knippel, A.: The $$k$$-partitioning problem: formulations and branch-and-cut. Networks 76(3), 323\u2013349 (2020)","journal-title":"Networks"},{"key":"221_CR4","first-page":"81","volume":"23","author":"M Altman","year":"1997","unstructured":"Altman, M.: The computational complexity of automated redistricting: is automation the answer? Rutgers Comput. Tech. LJ 23, 81 (1997)","journal-title":"Rutgers Comput. Tech. LJ"},{"issue":"1","key":"221_CR5","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1177\/1532673X17700611","volume":"46","author":"M Altman","year":"2018","unstructured":"Altman, M., McDonald, M.: Redistricting by formula: an Ohio reform experiment. Am. Polit. Res. 46(1), 103\u2013131 (2018)","journal-title":"Am. Polit. Res."},{"issue":"4","key":"221_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v042.i04","volume":"42","author":"M Altman","year":"2011","unstructured":"Altman, M., McDonald, M.P., et al.: BARD: Better automated redistricting. J. Stat. Soft. 42(4), 1\u201328 (2011)","journal-title":"J. Stat. Soft."},{"key":"221_CR7","doi-asserted-by":"crossref","DOI":"10.1090\/conm\/098","volume-title":"Every Planar Map is Four Colorable","author":"KI Appel","year":"1989","unstructured":"Appel, K.I., Haken, W.: Every Planar Map is Four Colorable, vol. 98. American Mathematical Society, Providence (1989)"},{"issue":"5","key":"221_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s00500-004-0413-4","volume":"9","author":"F Bacao","year":"2005","unstructured":"Bacao, F., Lobo, V., Painho, M.: Applying genetic algorithms to zone design. Soft. Comput. 9(5), 341\u2013348 (2005)","journal-title":"Soft. Comput."},{"key":"221_CR9","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/588","volume-title":"Graph Partitioning and Graph Clustering","author":"DA Bader","year":"2013","unstructured":"Bader, D.A., Meyerhenke, H., Sanders, P., Wagner, D.: Graph Partitioning and Graph Clustering, vol. 588. American Mathematical Society, Providence (2013)"},{"key":"221_CR10","doi-asserted-by":"crossref","unstructured":"Bar-Natan, A., Najt, L., Schutzman, Z.: The gerrymandering jumble: map projections permute districts\u2019 compactness scores. Cartogr. Geogr. Inf. Sci. 47(4), 321\u2013335 (2020)","DOI":"10.1080\/15230406.2020.1737575"},{"key":"221_CR11","doi-asserted-by":"crossref","unstructured":"Barnes, R., Solomon, J.: Gerrymandering and compactness: implementation flexibility and abuse. Political Anal. (2020) (to appear)","DOI":"10.1017\/pan.2020.36"},{"issue":"1","key":"221_CR12","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s12532-019-00171-5","volume":"12","author":"M Bastubbe","year":"2020","unstructured":"Bastubbe, M., L\u00fcbbecke, M.E.: A branch-and-price algorithm for capacitated hypergraph vertex separation. Math. Program. Comput. 12(1), 39\u201368 (2020)","journal-title":"Math. Program. Comput."},{"key":"221_CR13","unstructured":"Becker, A., Solomon, J.: Redistricting algorithms (2020)"},{"issue":"1","key":"221_CR14","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/s10878-014-9753-x","volume":"29","author":"W Ben-Ameur","year":"2015","unstructured":"Ben-Ameur, W., Mohamed-Sidi, M.A., Neto, J.: The $$k$$-separator problem: polyhedra, complexity and approximation results. J. Comb. Optim. 29(1), 276\u2013307 (2015)","journal-title":"J. Comb. Optim."},{"key":"221_CR15","volume-title":"Graph Partitioning","year":"2013","unstructured":"Bichot, C.E., Siarry, P. (eds.): Graph Partitioning. Wiley, New York (2013)"},{"issue":"1","key":"221_CR16","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1137\/S1052623497318682","volume":"9","author":"R Bornd\u00f6rfer","year":"1998","unstructured":"Bornd\u00f6rfer, R., Ferreira, C.E., Martin, A.: Decomposing matrices into blocks. SIAM J. Optim. 9(1), 236\u2013269 (1998)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"221_CR17","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/S0377-2217(01)00380-0","volume":"144","author":"B Bozkaya","year":"2003","unstructured":"Bozkaya, B., Erkut, E., Laporte, G.: A tabu search heuristic and adaptive memory procedure for political districting. Eur. J. Oper. Res. 144(1), 12\u201326 (2003)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"221_CR18","first-page":"163","volume":"8","author":"MH Browdy","year":"1990","unstructured":"Browdy, M.H.: Simulated annealing: an improved computer model for political redistricting. Yale Law Policy Rev. 8(1), 163\u2013179 (1990)","journal-title":"Yale Law Policy Rev."},{"key":"221_CR19","volume-title":"Redistricting: The Most Political Activity in America","author":"CS Bullock III","year":"2010","unstructured":"Bullock, C.S., III.: Redistricting: The Most Political Activity in America. Rowman & Littlefield Publishers, Lanham (2010)"},{"issue":"7","key":"221_CR20","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1016\/j.dam.2007.05.058","volume":"156","author":"M Camp\u00ealo","year":"2008","unstructured":"Camp\u00ealo, M., Campos, V.A., Corr\u00eaa, R.C.: On the asymmetric representatives formulation for the vertex coloring problem. Discrete Appl. Math. 156(7), 1097\u20131111 (2008)","journal-title":"Discrete Appl. Math."},{"issue":"4","key":"221_CR21","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1287\/opre.2013.1183","volume":"61","author":"R Carvajal","year":"2013","unstructured":"Carvajal, R., Constantino, M., Goycoolea, M., Vielma, J.P., Weintraub, A.: Imposing connectivity constraints in forest planning models. Oper. Res. 61(4), 824\u2013836 (2013)","journal-title":"Oper. Res."},{"key":"221_CR22","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.physa.2018.03.096","volume":"506","author":"WKT Cho","year":"2018","unstructured":"Cho, W.K.T., Liu, Y.Y.: Sampling from complicated and unknown distributions: Monte Carlo and Markov chain Monte Carlo methods for redistricting. Physica A 506, 170\u2013178 (2018)","journal-title":"Physica A"},{"issue":"1","key":"221_CR23","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/0166-218X(93)E0175-X","volume":"61","author":"S Chopra","year":"1995","unstructured":"Chopra, S., Rao, M.: Facets of the $$k$$-partition polytope. Discrete Appl. Math. 61(1), 27\u201348 (1995)","journal-title":"Discrete Appl. Math."},{"issue":"1\u20133","key":"221_CR24","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/BF01581239","volume":"59","author":"S Chopra","year":"1993","unstructured":"Chopra, S., Rao, M.R.: The partition problem. Math. Program. 59(1\u20133), 87\u2013115 (1993)","journal-title":"Math. Program."},{"issue":"4","key":"221_CR25","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1177\/0894439313484262","volume":"32","author":"C Chou","year":"2014","unstructured":"Chou, C., Kimbrough, S.O., Murphy, F.H., Sullivan-Fedock, J., Woodard, C.J.: On empirical validation of compactness measures for electoral redistricting and its significance for application of models in the social sciences. Soc. Sci. Comput. Rev. 32(4), 534\u2013543 (2014)","journal-title":"Soc. Sci. Comput. Rev."},{"key":"221_CR26","doi-asserted-by":"crossref","unstructured":"Cohen-Addad, V., Klein, P.N., Young, N.E.: Balanced centroidal power diagrams for redistricting. In: Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 389\u2013396. ACM (2018)","DOI":"10.1145\/3274895.3274979"},{"key":"221_CR27","unstructured":"Cohen-Addad, V., Klein, P.N., Marx, D.: On the computational tractability of a geographic clustering problem arising in redistricting. arXiv preprint arXiv:2009.00188 (2020)"},{"issue":"1","key":"221_CR28","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/BF01588779","volume":"49","author":"M Conforti","year":"1990","unstructured":"Conforti, M., Rao, M., Sassano, A.: The equipartition polytope. II: valid inequalities and facets. Math. Program. 49(1), 71\u201390 (1990)","journal-title":"Math. Program."},{"key":"221_CR29","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.disopt.2018.07.003","volume":"31","author":"D Cornaz","year":"2019","unstructured":"Cornaz, D., Furini, F., Lacroix, M., Malaguti, E., Mahjoub, A.R., Martin, S.: The vertex $$k$$-cut problem. Discrete Optim. 31, 8\u201328 (2019)","journal-title":"Discrete Optim."},{"key":"221_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21275-3","volume-title":"Parameterized Algorithms","author":"M Cygan","year":"2015","unstructured":"Cygan, M., Fomin, F.V., Kowalik, \u0141, Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Berlin (2015)"},{"issue":"4","key":"221_CR31","doi-asserted-by":"publisher","first-page":"864","DOI":"10.1137\/S0097539792225297","volume":"23","author":"E Dahlhaus","year":"1994","unstructured":"Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864\u2013894 (1994)","journal-title":"SIAM J. Comput."},{"issue":"1\u20132","key":"221_CR32","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1080\/00207543.2017.1401751","volume":"56","author":"MS Daskin","year":"2018","unstructured":"Daskin, M.S., Tucker, E.L.: The trade-off between the median and range of assigned demand in facility location models. Int. J. Prod. Res. 56(1\u20132), 97\u2013119 (2018)","journal-title":"Int. J. Prod. Res."},{"key":"221_CR33","unstructured":"DeFord, D.: Dual graphs for 2010 census units (2021). https:\/\/people.csail.mit.edu\/ddeford\/dual_graphs.html"},{"issue":"2","key":"221_CR34","first-page":"120","volume":"12","author":"D DeFord","year":"2019","unstructured":"DeFord, D., Duchin, M.: Redistricting reform in Virginia: districting criteria in context. Virginia Policy Rev. 12(2), 120\u2013146 (2019)","journal-title":"Virginia Policy Rev."},{"key":"221_CR35","doi-asserted-by":"publisher","unstructured":"DeFord, D., Duchin, M., Solomon, J.: Recombination: a family of Markov chains for redistricting. Harvard Data Science Rev. (2021). https:\/\/doi.org\/10.1162\/99608f92.eb30390f","DOI":"10.1162\/99608f92.eb30390f"},{"issue":"4","key":"221_CR36","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1137\/18M1215943","volume":"3","author":"D DeFord","year":"2019","unstructured":"DeFord, D., Lavenant, H., Schutzman, Z., Solomon, J.: Total variation isoperimetric profiles. SIAM J. Appl. Algebra Geometry 3(4), 585\u2013613 (2019)","journal-title":"SIAM J. Appl. Algebra Geometry"},{"issue":"4","key":"221_CR37","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1287\/moor.17.4.981","volume":"17","author":"M Deza","year":"1992","unstructured":"Deza, M., Gr\u00f6tschel, M., Laurent, M.: Clique-web facets for multicut polytopes. Math. Oper. Res. 17(4), 981\u20131000 (1992)","journal-title":"Math. Oper. Res."},{"key":"221_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-5559-1","volume-title":"Fundamentals of Parameterized Complexity","author":"RG Downey","year":"2013","unstructured":"Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity, vol. 4. Springer, Berlin (2013)"},{"key":"221_CR39","unstructured":"Dube, M., Clark, J.: Beyond the circle: Measuring district compactness using graph theory. In: Northeast Political Science Association Conference (2016)"},{"key":"221_CR40","unstructured":"Duchin, M., Strogatz, S.: Moon Duchin on fair voting and random walks. Quanta Magazine (2020). https:\/\/www.quantamagazine.org\/moon-duchin-on-fair-voting-and-random-walks-20200407\/"},{"key":"221_CR41","unstructured":"Duchin, M., Tenner, B.E.: Discrete geometry for electoral geography. arXiv preprint arXiv:1808.05860 (2018)"},{"issue":"2","key":"221_CR42","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/0166-218X(85)90008-3","volume":"10","author":"ME Dyer","year":"1985","unstructured":"Dyer, M.E., Frieze, A.M.: On the complexity of partitioning graphs into connected subgraphs. Discrete Appl. Math. 10(2), 139\u2013153 (1985)","journal-title":"Discrete Appl. Math."},{"key":"221_CR43","unstructured":"Eckstein, J.: Personal communication (2020)"},{"key":"221_CR44","doi-asserted-by":"crossref","unstructured":"Eisenbl\u00e4tter, A.: The semidefinite relaxation of the $$k$$-partition polytope is strong. In: International Conference on Integer Programming and Combinatorial Optimization, pp. 273\u2013290. Springer (2002)","DOI":"10.1007\/3-540-47867-1_20"},{"key":"221_CR45","unstructured":"Faenza, Y.: Personal communication (2021)"},{"issue":"3","key":"221_CR46","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1287\/moor.1090.0392","volume":"34","author":"Y Faenza","year":"2009","unstructured":"Faenza, Y., Kaibel, V.: Extended formulations for packing and partitioning orbitopes. Math. Oper. Res. 34(3), 686\u2013697 (2009)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"221_CR47","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/BF02592198","volume":"74","author":"CE Ferreira","year":"1996","unstructured":"Ferreira, C.E., Martin, A., de Souza, C.C., Weismantel, R., Wolsey, L.A.: Formulations and valid inequalities for the node capacitated graph partitioning problem. Math. Program. 74(3), 247\u2013266 (1996)","journal-title":"Math. Program."},{"issue":"2","key":"221_CR48","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/BF01581107","volume":"81","author":"CE Ferreira","year":"1998","unstructured":"Ferreira, C.E., Martin, A., de Souza, C.C., Weismantel, R., Wolsey, L.A.: The node capacitated graph partitioning problem: a computational study. Math. Program. 81(2), 229\u2013256 (1998)","journal-title":"Math. Program."},{"key":"221_CR49","unstructured":"Fifield, B., Higgins, M., Imai, K., Tarr, A.: A new automated redistricting simulator using Markov chain Monte Carlo. Work. Pap. Princeton University Press, Princeton (2015)"},{"issue":"2","key":"221_CR50","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s12532-016-0111-0","volume":"9","author":"M Fischetti","year":"2017","unstructured":"Fischetti, M., Leitner, M., Ljubi\u0107, I., Luipersbeck, M., Monaci, M., Resch, M., Salvagnin, D., Sinnl, M.: Thinning out Steiner trees: a node-based model for uniform edge costs. Math. Program. Comput. 9(2), 203\u2013229 (2017)","journal-title":"Math. Program. Comput."},{"key":"221_CR51","doi-asserted-by":"crossref","unstructured":"Fischetti, M., Lodi, A., Salvagnin, D.: Just MIP it! In: Matheuristics, pp. 39\u201370. Springer (2009)","DOI":"10.1007\/978-1-4419-1306-7_2"},{"issue":"2","key":"221_CR52","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s12532-019-00167-1","volume":"12","author":"F Furini","year":"2020","unstructured":"Furini, F., Ljubi\u0107, I., Malaguti, E., Paronuzzi, P.: On integer and bilevel formulations for the $$k$$-vertex cut problem. Math. Program. Comput. 12(2), 133\u2013164 (2020)","journal-title":"Math. Program. Comput."},{"key":"221_CR53","unstructured":"Furini, F., Ljubi\u0107, I., Malaguti, E., Paronuzzi, P.: Casting light on the hidden bilevel combinatorial structure of the capacitated vertex separator problem. Oper. Res. (2021) (to appear)"},{"key":"221_CR54","doi-asserted-by":"crossref","unstructured":"Garfinkel, R.S., Nemhauser, G.L.: Optimal political districting by implicit enumeration techniques. Manag. Sci. 16(8), B-495 (1970)","DOI":"10.1287\/mnsc.16.8.B495"},{"key":"221_CR55","doi-asserted-by":"crossref","unstructured":"Gleixner, A., Hendel, G., Gamrath, G., Achterberg, T., Bastubbe, M., Berthold, T., Christophel, P., Jarck, K., Koch, T., Linderoth, J., et\u00a0al.: MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library. Math. Program. Comput. (2021) (to appear)","DOI":"10.1007\/s12532-020-00194-3"},{"key":"221_CR56","unstructured":"Goderbauer, S., Winandy, J.: Political districting problem: Literature review and discussion with regard to federal elections in Germany (2018). https:\/\/www.or.rwth-aachen.de\/files\/research\/repORt\/LitSurvey_PoliticalDistricting__Goderbauer_Winandy_20181024.pdf"},{"issue":"1","key":"221_CR57","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1002\/net.3230230104","volume":"23","author":"MX Goemans","year":"1993","unstructured":"Goemans, M.X., Myung, Y.S.: A catalog of Steiner tree formulations. Networks 23(1), 19\u201328 (1993)","journal-title":"Networks"},{"issue":"1","key":"221_CR58","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1287\/moor.19.1.24","volume":"19","author":"O Goldschmidt","year":"1994","unstructured":"Goldschmidt, O., Hochbaum, D.S.: A polynomial algorithm for the $$k$$-cut problem for fixed $$k$$. Math. Oper. Res. 19(1), 24\u201337 (1994)","journal-title":"Math. Oper. Res."},{"issue":"5","key":"221_CR59","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1287\/inte.2013.0697","volume":"43","author":"R Gopalan","year":"2013","unstructured":"Gopalan, R., Kimbrough, S.O., Murphy, F.H., Quintus, N.: The Philadelphia districting contest: designing territories for city council based upon the 2010 census. Interfaces 43(5), 477\u2013489 (2013)","journal-title":"Interfaces"},{"key":"221_CR60","first-page":"77","volume":"33","author":"B Grofman","year":"1985","unstructured":"Grofman, B.: Criteria for districting: a social science perspective. UCLA L. Rev. 33, 77 (1985)","journal-title":"UCLA L. Rev."},{"issue":"1","key":"221_CR61","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/BF01589097","volume":"45","author":"M Gr\u00f6tschel","year":"1989","unstructured":"Gr\u00f6tschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45(1), 59\u201396 (1989)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR62","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/BF01580870","volume":"47","author":"M Gr\u00f6tschel","year":"1990","unstructured":"Gr\u00f6tschel, M., Wakabayashi, Y.: Facets of the clique partitioning polytope. Math. Program. 47(1), 367\u2013387 (1990)","journal-title":"Math. Program."},{"issue":"4","key":"221_CR63","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.jvlc.2011.03.001","volume":"22","author":"D Guo","year":"2011","unstructured":"Guo, D., Jin, H.: iRedistrict: Geovisual analytics for redistricting optimization. J. Vis. Lang. Comput. 22(4), 279\u2013289 (2011)","journal-title":"J. Vis. Lang. Comput."},{"key":"221_CR64","doi-asserted-by":"crossref","unstructured":"Gurnee, W., Shmoys, D.B.: Fairmandering: a column generation heuristic for fairness-optimized political districting. arXiv preprint arXiv:2103.11469 (2021)","DOI":"10.1137\/1.9781611976830.9"},{"key":"221_CR65","doi-asserted-by":"crossref","unstructured":"Guti\u00e9rrez-Andrade, M.\u00c1., Rinc\u00f3n-Garc\u00eda, E.A., de-los Cobos-Silva, S.G., Lara-Vel\u00e1zquez, P., Mora-Guti\u00e9rrez, R.A., Ponsich, A.: Simulated annealing and artificial bee colony for the redistricting process in Mexico. INFORMS J. Appl. Anal. 49(3), 189\u2013200 (2019)","DOI":"10.1287\/inte.2019.0992"},{"issue":"1","key":"221_CR66","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF02614317","volume":"79","author":"P Hansen","year":"1997","unstructured":"Hansen, P., Jaumard, B.: Cluster analysis and mathematical programming. Math. Program. 79(1), 191\u2013215 (1997)","journal-title":"Math. Program."},{"issue":"3","key":"221_CR67","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/S0166-218X(98)00036-5","volume":"85","author":"D Hartvigsen","year":"1998","unstructured":"Hartvigsen, D.: The planar multiterminal cut problem. Discrete Appl. Math. 85(3), 203\u2013222 (1998)","journal-title":"Discrete Appl. Math."},{"key":"221_CR68","unstructured":"Hebert, J.G., Vandenberg, M.E., Smith, P.: The Realist\u2019s Guide to Redistricting: Avoiding the Legal Pitfalls. American Bar Association (2010)"},{"issue":"6","key":"221_CR69","doi-asserted-by":"publisher","first-page":"998","DOI":"10.1287\/opre.13.6.998","volume":"13","author":"S Hess","year":"1965","unstructured":"Hess, S., Weaver, J., Siegfeldt, H., Whelan, J., Zitlau, P.: Nonpartisan political redistricting by computer. Oper. Res. 13(6), 998\u20131006 (1965)","journal-title":"Oper. Res."},{"key":"221_CR70","unstructured":"Hettle, C., Zhu, S., Gupta, S., Xie, Y.: Balanced districting on grid graphs with provable compactness and contiguity. arXiv preprint arXiv:2102.05028 (2021)"},{"issue":"12","key":"221_CR71","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1016\/S0305-0548(96)00029-9","volume":"23","author":"M Hojati","year":"1996","unstructured":"Hojati, M.: Optimal political districting. Comput. Oper. Res. 23(12), 1147\u20131161 (1996)","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"221_CR72","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s12532-020-00186-3","volume":"13","author":"C Hojny","year":"2021","unstructured":"Hojny, C., Joormann, I., L\u00fcthen, H., Schmidt, M.: Mixed-integer programming techniques for the connected max-$$k$$-cut problem. Math. Program. Comput. 13(1), 75\u2013132 (2021)","journal-title":"Math. Program. Comput."},{"issue":"1\u20132","key":"221_CR73","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s10107-018-1239-7","volume":"175","author":"C Hojny","year":"2019","unstructured":"Hojny, C., Pfetsch, M.E.: Polytopes associated with symmetry handling. Math. Program. 175(1\u20132), 197\u2013240 (2019)","journal-title":"Math. Program."},{"issue":"1\u20133","key":"221_CR74","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF01585164","volume":"62","author":"EL Johnson","year":"1993","unstructured":"Johnson, E.L., Mehrotra, A., Nemhauser, G.L.: Min-cut clustering. Math. Program. 62(1\u20133), 133\u2013151 (1993)","journal-title":"Math. Program."},{"issue":"4","key":"221_CR75","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.disopt.2011.07.001","volume":"8","author":"V Kaibel","year":"2011","unstructured":"Kaibel, V., Peinhardt, M., Pfetsch, M.E.: Orbitopal fixing. Discrete Optim. 8(4), 595\u2013610 (2011)","journal-title":"Discrete Optim."},{"issue":"1","key":"221_CR76","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-006-0081-5","volume":"114","author":"V Kaibel","year":"2008","unstructured":"Kaibel, V., Pfetsch, M.: Packing and partitioning orbitopes. Math. Program. 114(1), 1\u201336 (2008)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR77","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/s00453-010-9436-7","volume":"61","author":"H Kaplan","year":"2011","unstructured":"Kaplan, H., Nussbaum, Y.: Maximum flow in directed planar graphs with vertex capacities. Algorithmica 61(1), 174\u2013189 (2011)","journal-title":"Algorithmica"},{"key":"221_CR78","unstructured":"Kaufman, A., King, G., Komisarchik, M.: How to measure legislative district compactness if you only know it when you see it. Am. J. Polit. Sci. (forthcoming)"},{"issue":"4","key":"221_CR79","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4018\/IJAGR.2017100101","volume":"8","author":"M Kim","year":"2017","unstructured":"Kim, M., Xiao, N.: Contiguity-based optimization models for political redistricting problems. Int. J. Appl. Geospatial Res. (IJAGR) 8(4), 1\u201318 (2017)","journal-title":"Int. J. Appl. Geospatial Res. (IJAGR)"},{"key":"221_CR80","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/s41324-019-00254-4","volume":"27","author":"MJ Kim","year":"2019","unstructured":"Kim, M.J.: Give-and-take heuristic model to political redistricting problems. Spat. Inf. Res. 27, 539\u2013552 (2019)","journal-title":"Spat. Inf. Res."},{"issue":"1\u20132","key":"221_CR81","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10107-014-0762-4","volume":"149","author":"DM King","year":"2015","unstructured":"King, D.M., Jacobson, S.H., Sewell, E.C.: Efficient geo-graph contiguity and hole algorithms for geographic zoning and dynamic plane graph partitioning. Math. Program. 149(1\u20132), 425\u2013457 (2015)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR82","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10589-017-9936-3","volume":"69","author":"DM King","year":"2018","unstructured":"King, D.M., Jacobson, S.H., Sewell, E.C.: The geo-graph in practice: creating United States congressional districts from census blocks. Comput. Optim. Appl. 69(1), 25\u201349 (2018)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"221_CR83","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1287\/opre.1120.1083","volume":"60","author":"DM King","year":"2012","unstructured":"King, D.M., Jacobson, S.H., Sewell, E.C., Cho, W.K.T.: Geo-graphs: an efficient model for enforcing contiguity and hole constraints in planar graph partitioning. Oper. Res. 60(5), 1213\u20131228 (2012)","journal-title":"Oper. Res."},{"issue":"24","key":"221_CR84","doi-asserted-by":"publisher","first-page":"3473","DOI":"10.1016\/j.disc.2010.08.009","volume":"310","author":"M Labb\u00e9","year":"2010","unstructured":"Labb\u00e9, M., \u00d6zsoy, F.A.: Size-constrained graph partitioning polytopes. Discrete Math. 310(24), 3473\u20133493 (2010)","journal-title":"Discrete Math."},{"key":"221_CR85","doi-asserted-by":"crossref","unstructured":"Lacki, J., Nussbaum, Y., Sankowski, P., Wulff-Nilsen, C.: Single source\u2013all sinks max flows in planar digraphs. In: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (focs), pp. 599\u2013608. IEEE (2012)","DOI":"10.1109\/FOCS.2012.66"},{"key":"221_CR86","doi-asserted-by":"crossref","unstructured":"Lee, E.: Partitioning a graph into small pieces with applications to path transversal. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1546\u20131558. SIAM (2017)","DOI":"10.1137\/1.9781611974782.101"},{"issue":"1","key":"221_CR87","first-page":"1","volume":"24","author":"HA Levin","year":"2019","unstructured":"Levin, H.A., Friedler, S.A.: Automated congressional redistricting. J. Exp. Algorithmics (JEA) 24(1), 1\u201310 (2019)","journal-title":"J. Exp. Algorithmics (JEA)"},{"key":"221_CR88","unstructured":"Levitt, J.: A citizen\u2019s guide to redistricting. Brennan Center for Justice at New York University School of Law (2010)"},{"issue":"2","key":"221_CR89","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/0022-0000(80)90060-4","volume":"20","author":"JM Lewis","year":"1980","unstructured":"Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comput. Syst. Sci. 20(2), 219\u2013230 (1980)","journal-title":"J. Comput. Syst. Sci."},{"key":"221_CR90","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.swevo.2016.04.004","volume":"30","author":"YY Liu","year":"2016","unstructured":"Liu, Y.Y., Cho, W.K.T., Wang, S.: PEAR: a massively parallel evolutionary computation approach for political redistricting optimization and analysis. Swarm Evol. Comput. 30, 78\u201392 (2016)","journal-title":"Swarm Evol. Comput."},{"key":"221_CR91","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/S0927-0507(05)80126-4","volume":"7","author":"TL Magnanti","year":"1995","unstructured":"Magnanti, T.L., Wolsey, L.A.: Optimal trees. Handbooks Oper. Res. Manag. Sci. 7, 503\u2013615 (1995)","journal-title":"Handbooks Oper. Res. Manag. Sci."},{"issue":"1","key":"221_CR92","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10107-002-0358-2","volume":"94","author":"F Margot","year":"2002","unstructured":"Margot, F.: Pruning by isomorphism in branch-and-cut. Math. Program. 94(1), 71\u201390 (2002)","journal-title":"Math. Program."},{"issue":"1\u20133","key":"221_CR93","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-003-0394-6","volume":"98","author":"F Margot","year":"2003","unstructured":"Margot, F.: Exploiting orbits in symmetric ILP. Math. Program. 98(1\u20133), 3\u201321 (2003)","journal-title":"Math. Program."},{"issue":"2\u20133","key":"221_CR94","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s10107-002-0316-z","volume":"94","author":"F Margot","year":"2003","unstructured":"Margot, F.: Small covering designs by branch-and-cut. Math. Program. 94(2\u20133), 207\u2013220 (2003)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR95","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.disopt.2006.10.008","volume":"4","author":"F Margot","year":"2007","unstructured":"Margot, F.: Symmetric ILP: coloring and small integers. Discrete Optim. 4(1), 40\u201362 (2007)","journal-title":"Discrete Optim."},{"key":"221_CR96","doi-asserted-by":"crossref","unstructured":"Margot, F.: Symmetry in integer linear programming. In: 50 Years of Integer Programming 1958-2008, pp. 647\u2013686. Springer (2010)","DOI":"10.1007\/978-3-540-68279-0_17"},{"issue":"8","key":"221_CR97","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1287\/mnsc.44.8.1100","volume":"44","author":"A Mehrotra","year":"1998","unstructured":"Mehrotra, A., Johnson, E.L., Nemhauser, G.L.: An optimization based heuristic for political districting. Manag. Sci. 44(8), 1100\u20131114 (1998)","journal-title":"Manag. Sci."},{"issue":"1","key":"221_CR98","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-6377(98)00006-6","volume":"22","author":"A Mehrotra","year":"1998","unstructured":"Mehrotra, A., Trick, M.A.: Cliques and clustering: a combinatorial approach. Oper. Res. Lett. 22(1), 1\u201312 (1998)","journal-title":"Oper. Res. Lett."},{"key":"221_CR99","unstructured":"MGGG: GerryChain 0.2.12. (2021). https:\/\/gerrychain.readthedocs.io\/en\/latest\/"},{"key":"221_CR100","unstructured":"Miller, S.: The problem of redistricting: the use of centroidal Voronoi diagrams to build unbiased congressional districts. Senior project, Whitman College (2007)"},{"key":"221_CR101","doi-asserted-by":"crossref","unstructured":"Miyazawa, F.K., Moura, P.F., Ota, M.J., Wakabayashi, Y.: Partitioning a graph into balanced connected classes: formulations, separation and experiments. Eur. J. Oper. Res. (2021) (to appear)","DOI":"10.1016\/j.ejor.2020.12.059"},{"key":"221_CR102","doi-asserted-by":"publisher","first-page":"863","DOI":"10.2307\/1226994","volume":"17","author":"SS Nagel","year":"1964","unstructured":"Nagel, S.S.: Simplified bipartisan computer redistricting. Stan. L. Rev. 17, 863 (1964)","journal-title":"Stan. L. Rev."},{"issue":"4","key":"221_CR103","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.2307\/2131686","volume":"52","author":"RG Niemi","year":"1990","unstructured":"Niemi, R.G., Grofman, B., Carlucci, C., Hofeller, T.: Measuring compactness and the role of a compactness standard in a test for partisan and racial gerrymandering. J. Polit. 52(4), 1155\u20131181 (1990)","journal-title":"J. Polit."},{"issue":"15","key":"221_CR104","first-page":"89","volume":"2017","author":"J Oehrlein","year":"2017","unstructured":"Oehrlein, J., Haunert, J.H.: A cutting-plane method for contiguity-constrained spatial aggregation. J. Spatial Inf. Sci. 2017(15), 89\u2013120 (2017)","journal-title":"J. Spatial Inf. Sci."},{"key":"221_CR105","unstructured":"Olson, B.: Impartial automatic redistricting. https:\/\/bdistricting.com\/2010\/ (2019). Accessed 21 June 2019"},{"issue":"4","key":"221_CR106","first-page":"209","volume":"38","author":"M Oosten","year":"2001","unstructured":"Oosten, M., Rutten, J.H., Spieksma, F.C.: The clique partitioning problem: facets and patching facets. Networks Int. J. 38(4), 209\u2013226 (2001)","journal-title":"Networks Int. J."},{"issue":"1","key":"221_CR107","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1111\/j.1467-9574.2007.00350.x","volume":"61","author":"M Oosten","year":"2007","unstructured":"Oosten, M., Rutten, J.H., Spieksma, F.C.: Disconnecting graphs by removing vertices: a polyhedral approach. Stat. Neerl. 61(1), 35\u201360 (2007)","journal-title":"Stat. Neerl."},{"issue":"1","key":"221_CR108","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s10107-014-0812-y","volume":"150","author":"J Ostrowski","year":"2015","unstructured":"Ostrowski, J., Anjos, M.F., Vannelli, A.: Modified orbital branching for structured symmetry with an application to unit commitment. Math. Program. 150(1), 99\u2013129 (2015)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR109","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s10107-009-0273-x","volume":"126","author":"J Ostrowski","year":"2011","unstructured":"Ostrowski, J., Linderoth, J., Rossi, F., Smriglio, S.: Orbital branching. Math. Program. 126(1), 147\u2013178 (2011)","journal-title":"Math. Program."},{"key":"221_CR110","unstructured":"Pfetsch, M.: Personal communication (2021)"},{"issue":"1","key":"221_CR111","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s12532-018-0140-y","volume":"11","author":"ME Pfetsch","year":"2019","unstructured":"Pfetsch, M.E., Rehn, T.: A computational comparison of symmetry handling methods for mixed integer programs. Math. Program. Comput. 11(1), 37\u201393 (2019)","journal-title":"Math. Program. Comput."},{"key":"221_CR112","doi-asserted-by":"crossref","unstructured":"Pildes, R.H., Niemi, R.G.: Expressive harms, \u201cbizarre districts,\u201d and voting rights: Evaluating election-district appearances after Shaw v. Reno. Michigan Law Review 92(3), 483\u2013587 (1993)","DOI":"10.2307\/1289795"},{"key":"221_CR113","doi-asserted-by":"crossref","unstructured":"Polsby, D.D., Popper, R.D.: The third criterion: Compactness as a procedural safeguard against partisan gerrymandering. Yale L. & Pol\u2019y Rev. 9, 301 (1991)","DOI":"10.2139\/ssrn.2936284"},{"key":"221_CR114","doi-asserted-by":"publisher","first-page":"652","DOI":"10.2307\/1289797","volume":"92","author":"DD Polsby","year":"1993","unstructured":"Polsby, D.D., Popper, R.D.: Ugly: An inquiry into the problem of racial gerrymandering under the Voting Rights Act. Mich. L. Rev. 92, 652 (1993)","journal-title":"Mich. L. Rev."},{"key":"221_CR115","unstructured":"Rehfeldt, D., Franz, H., Koch, T.: Optimal connected subgraphs: Formulations and algorithms. Tech. Rep. 20-23, ZIB, Takustr. 7, 14195 Berlin (2020)"},{"issue":"1","key":"221_CR116","doi-asserted-by":"publisher","first-page":"70","DOI":"10.2307\/2109043","volume":"5","author":"EC Reock","year":"1961","unstructured":"Reock, E.C.: A note: measuring compactness as a requirement of legislative apportionment. Midwest J. Polit. Sci. 5(1), 70\u201374 (1961)","journal-title":"Midwest J. Polit. Sci."},{"issue":"9\u201310","key":"221_CR117","doi-asserted-by":"publisher","first-page":"1468","DOI":"10.1016\/j.mcm.2008.05.041","volume":"48","author":"F Ricca","year":"2008","unstructured":"Ricca, F., Scozzari, A., Simeone, B.: Weighted Voronoi region algorithms for political districting. Math. Comput. Model. 48(9\u201310), 1468\u20131477 (2008)","journal-title":"Math. Comput. Model."},{"issue":"1","key":"221_CR118","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s10479-012-1267-2","volume":"204","author":"F Ricca","year":"2013","unstructured":"Ricca, F., Scozzari, A., Simeone, B.: Political districting: from classical models to recent approaches. Ann. Oper. Res. 204(1), 271\u2013299 (2013)","journal-title":"Ann. Oper. Res."},{"issue":"3","key":"221_CR119","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1016\/j.ejor.2006.08.065","volume":"189","author":"F Ricca","year":"2008","unstructured":"Ricca, F., Simeone, B.: Local search algorithms for political districting. Eur. J. Oper. Res. 189(3), 1409\u20131426 (2008)","journal-title":"Eur. J. Oper. Res."},{"issue":"3","key":"221_CR120","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1007\/s12532-020-00175-6","volume":"12","author":"H Salemi","year":"2020","unstructured":"Salemi, H., Buchanan, A.: Parsimonious formulations for low-diameter clusters. Math. Program. Comput. 12(3), 493\u2013528 (2020)","journal-title":"Math. Program. Comput."},{"key":"221_CR121","unstructured":"Schwartz, S.: An overview of graph covering and partitioning. Tech. Rep. 20-24, ZIB, Takustr. 7, 14195 Berlin (2020)"},{"key":"221_CR122","first-page":"443","volume":"50","author":"JE Schwartzberg","year":"1965","unstructured":"Schwartzberg, J.E.: Reapportionment, gerrymanders, and the notion of compactness. Minn. L. Rev. 50, 443 (1965)","journal-title":"Minn. L. Rev."},{"issue":"3","key":"221_CR123","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.disopt.2012.07.001","volume":"9","author":"S Shen","year":"2012","unstructured":"Shen, S., Smith, J.C., Goli, R.: Exact interdiction models and algorithms for disconnecting networks via node deletions. Discrete Optim. 9(3), 172\u2013188 (2012)","journal-title":"Discrete Optim."},{"issue":"1","key":"221_CR124","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1111\/j.1538-4632.2005.00605.x","volume":"37","author":"T Shirabe","year":"2005","unstructured":"Shirabe, T.: A model of contiguity for spatial unit allocation. Geogr. Anal. 37(1), 2\u201316 (2005)","journal-title":"Geogr. Anal."},{"issue":"6","key":"221_CR125","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1068\/b34104","volume":"36","author":"T Shirabe","year":"2009","unstructured":"Shirabe, T.: Districting modeling with exact contiguity constraints. Environ. Plann. B. Plann. Des. 36(6), 1053\u20131066 (2009)","journal-title":"Environ. Plann. B. Plann. Des."},{"issue":"2","key":"221_CR126","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.disopt.2006.08.001","volume":"4","author":"MM S\u00f8rensen","year":"2007","unstructured":"S\u00f8rensen, M.M.: Facet-defining inequalities for the simple graph partitioning polytope. Discrete Optim. 4(2), 221\u2013231 (2007)","journal-title":"Discrete Optim."},{"key":"221_CR127","doi-asserted-by":"publisher","unstructured":"Suwal, B., Sun, M., Rule, P.: mggg\/GerryChainJulia: v0.1.2 (2020). https:\/\/doi.org\/10.5281\/zenodo.4111000","DOI":"10.5281\/zenodo.4111000"},{"issue":"3","key":"221_CR128","first-page":"313","volume":"28","author":"L Svec","year":"2007","unstructured":"Svec, L., Burden, S., Dilley, A.: Applying Voronoi diagrams to the redistricting problem. UMAP J. 28(3), 313\u2013329 (2007)","journal-title":"UMAP J."},{"key":"221_CR129","unstructured":"Swamy, R., King, D.M., Jacobson, S.H.: A case for transparency in the design of political districts (2019). Working paper"},{"key":"221_CR130","unstructured":"Swamy, R., King, D.M., Jacobson, S.H.: Multi-objective optimization for political districting: a scalable multilevel approach (2019). http:\/\/www.optimization-online.org\/DB_FILE\/2019\/03\/7123.pdf. Working paper"},{"key":"221_CR131","doi-asserted-by":"publisher","unstructured":"Validi, H., Buchanan, A.: Political districting to minimize cut edges (2022). https:\/\/doi.org\/10.5281\/zenodo.6374373","DOI":"10.5281\/zenodo.6374373"},{"key":"221_CR132","doi-asserted-by":"crossref","unstructured":"Validi, H., Buchanan, A., Lykhovyd, E.: Imposing contiguity constraints in political districting models. Oper. Res. (to appear) (2021)","DOI":"10.1287\/opre.2021.2141"},{"issue":"1","key":"221_CR133","doi-asserted-by":"publisher","first-page":"105","DOI":"10.2307\/2145973","volume":"76","author":"W Vickrey","year":"1961","unstructured":"Vickrey, W.: On the prevention of gerrymandering. Polit. Sci. Q. 76(1), 105\u2013110 (1961)","journal-title":"Polit. Sci. Q."},{"issue":"1\u20132","key":"221_CR134","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s10107-017-1117-8","volume":"166","author":"Y Wang","year":"2017","unstructured":"Wang, Y., Buchanan, A., Butenko, S.: On imposing connectivity constraints in integer programs. Math. Program. 166(1\u20132), 241\u2013271 (2017)","journal-title":"Math. Program."},{"issue":"1","key":"221_CR135","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1111\/j.1435-5597.1995.tb00626.x","volume":"74","author":"JC Williams Jr","year":"1995","unstructured":"Williams, J.C., Jr.: Political redistricting: a review. Pap. Reg. Sci. 74(1), 13\u201340 (1995)","journal-title":"Pap. Reg. Sci."},{"issue":"4","key":"221_CR136","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1007\/s00224-009-9215-5","volume":"46","author":"M Xiao","year":"2010","unstructured":"Xiao, M.: Simple and improved parameterized algorithms for multiterminal cuts. Theory Comput. Syst. 46(4), 723\u2013736 (2010)","journal-title":"Theory Comput. Syst."},{"key":"221_CR137","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.jcss.2017.04.004","volume":"88","author":"M Xiao","year":"2017","unstructured":"Xiao, M.: Linear kernels for separating a graph into components of bounded size. J. Comput. Syst. Sci. 88, 260\u2013270 (2017)","journal-title":"J. Comput. Syst. Sci."},{"issue":"1","key":"221_CR138","doi-asserted-by":"publisher","first-page":"105","DOI":"10.2307\/439947","volume":"13","author":"HP Young","year":"1988","unstructured":"Young, H.P.: Measuring the compactness of legislative districts. Legis. Stud. Q. 13(1), 105\u2013115 (1988)","journal-title":"Legis. Stud. Q."}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-022-00221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12532-022-00221-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-022-00221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,13]],"date-time":"2022-11-13T06:18:35Z","timestamp":1668320315000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12532-022-00221-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,26]]},"references-count":138,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["221"],"URL":"https:\/\/doi.org\/10.1007\/s12532-022-00221-5","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,26]]},"assertion":[{"value":"23 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The code is publicly available on GitHub at .","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}