{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T04:16:43Z","timestamp":1751516203243,"version":"3.41.0"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319774039"},{"type":"electronic","value":"9783319774046"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-77404-6_56","type":"book-chapter","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T10:03:11Z","timestamp":1520848991000},"page":"777-789","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reactive Proximity Data Structures for Graphs"],"prefix":"10.1007","author":[{"given":"David","family":"Eppstein","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael T.","family":"Goodrich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nil","family":"Mamano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,13]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Agarwal, P.K., Eppstein, D., Matou\u0161ek, J.: Dynamic half-space reporting, geometric optimization, and minimum spanning trees. In: 33rd Symposium Foundations of Computer Science (FOCS), pp. 80\u201389 (1992)","key":"56_CR1","DOI":"10.1109\/SFCS.1992.267816"},{"issue":"4","key":"56_CR2","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/j.ipl.2008.10.003","volume":"109","author":"EM Arkin","year":"2009","unstructured":"Arkin, E.M., Bae, S.W., Efrat, A., Okamoto, K., Mitchell, J.S., Polishchuk, V.: Geometric stable roommates. Inf. Process. Lett. 109(4), 219\u2013224 (2009). http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020019008003098","journal-title":"Inf. Process. Lett."},{"issue":"3","key":"56_CR3","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1145\/116873.116880","volume":"23","author":"F Aurenhammer","year":"1991","unstructured":"Aurenhammer, F.: Voronoi diagrams\u2013a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345\u2013405 (1991)","journal-title":"ACM Comput. Surv."},{"issue":"2","key":"56_CR4","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1287\/ijoc.1070.0231","volume":"20","author":"LS Buriol","year":"2008","unstructured":"Buriol, L.S., Resende, M.G.C., Thorup, M.: Speeding up dynamic shortest-path algorithms. INFORMS J. Comput. 20(2), 191\u2013204 (2008)","journal-title":"INFORMS J. Comput."},{"issue":"4","key":"56_CR5","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1109\/TC.2008.198","volume":"58","author":"EPF Chan","year":"2009","unstructured":"Chan, E.P.F., Yang, Y.: Shortest path tree computation in dynamic graphs. IEEE Trans. Comput. 58(4), 541\u2013557 (2009)","journal-title":"IEEE Trans. Comput."},{"issue":"3","key":"56_CR6","doi-asserted-by":"publisher","first-page":"16:1","DOI":"10.1145\/1706591.1706596","volume":"57","author":"TM Chan","year":"2010","unstructured":"Chan, T.M.: A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries. J. ACM 57(3), 16:1\u201316:15 (2010)","journal-title":"J. ACM"},{"unstructured":"Chung, F.R.K.: Separator theorems and their applications. In: Paths, flows, and VLSI-layout (Bonn, 1988), Algorithms Combin. vol. 9, pp. 17\u201334. Springer, Berlin (1990)","key":"56_CR7"},{"doi-asserted-by":"crossref","unstructured":"Clarkson, K.L.: Nearest-neighbor searching and metric space dimensions. In: Shakhnarovich, G., Darrell, T., Indyk, P. (eds.) Nearest-Neighbor Methods in Learning and Vision: Theory and Practice, pp. 15\u201359. MIT Press (2006). Chapter 2","key":"56_CR8","DOI":"10.7551\/mitpress\/4908.003.0005"},{"key":"56_CR9","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2001","unstructured":"Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill, New York City (2001)","edition":"2"},{"key":"56_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-77974-2","volume-title":"Computational Geometry: Introduction","author":"M De Berg","year":"2008","unstructured":"De Berg, M., Cheong, O., Van Kreveld, M., Overmars, M.: Computational Geometry: Introduction. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-77974-2"},{"unstructured":"Demetrescu, C., Goldberg, A.V., Johnson, D.S.: 9th DIMACS implementation challenge: shortest paths (2006). http:\/\/www.dis.uniroma1.it\/~challenge9\/","key":"56_CR11"},{"issue":"6","key":"56_CR12","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1145\/1039488.1039492","volume":"51","author":"C Demetrescu","year":"2004","unstructured":"Demetrescu, C., Italiano, G.F.: A new approach to dynamic all pairs shortest paths. J. ACM 51(6), 968\u2013992 (2004)","journal-title":"J. ACM"},{"key":"56_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/3-540-59042-0_73","volume-title":"STACS 95","author":"HN Djidjev","year":"1995","unstructured":"Djidjev, H.N., Pantziou, G.E., Zaroliagis, C.D.: On-line and dynamic algorithms for shortest path problems. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 193\u2013204. Springer, Heidelberg (1995). https:\/\/doi.org\/10.1007\/3-540-59042-0_73"},{"issue":"2","key":"56_CR14","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1137\/16M1062879","volume":"31","author":"V Dujmovi\u0107","year":"2017","unstructured":"Dujmovi\u0107, V., Eppstein, D., Wood, D.R.: Structure of graphs with locally restricted crossings. SIAM J. Discrete Math. 31(2), 805\u2013824 (2017)","journal-title":"SIAM J. Discrete Math."},{"issue":"2","key":"56_CR15","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1137\/15M1017569","volume":"30","author":"Z Dvo\u0159\u00e1k","year":"2016","unstructured":"Dvo\u0159\u00e1k, Z., Norin, S.: Strongly sublinear separators and polynomial expansion. SIAM J. Discrete Math. 30(2), 1095\u20131101 (2016)","journal-title":"SIAM J. Discrete Math."},{"doi-asserted-by":"crossref","unstructured":"van Emde Boas, P.: Preserving order in a forest in less than logarithmic time. In: 16th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 75\u201384 (1975)","key":"56_CR16","DOI":"10.1109\/SFCS.1975.26"},{"issue":"1","key":"56_CR17","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF02574030","volume":"13","author":"D Eppstein","year":"1995","unstructured":"Eppstein, D.: Dynamic Euclidean minimum spanning trees and extrema of binary functions. Discrete Comput. Geom. 13(1), 111\u2013122 (1995)","journal-title":"Discrete Comput. Geom."},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D.: Fast hierarchical clustering and other applications of dynamic closest pairs. J. Exp. Algorithmics 5 (2000)","key":"56_CR18","DOI":"10.1145\/351827.351829"},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D.: All maximal independent sets and dynamic dominance for sparse graphs. ACM Trans. Algorithms 5(4), Article No. 38 (2009)","key":"56_CR19","DOI":"10.1145\/1597036.1597042"},{"unstructured":"Eppstein, D.: Treetopes and their graphs. In: 27th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 969\u2013984 (2016). http:\/\/dl.acm.org\/citation.cfm?id=2884435.2884504","key":"56_CR20"},{"unstructured":"Eppstein, D., Galil, Z., Italiano, G.F.: Dynamic graph algorithms. In: Atallah, M.J. (ed.) Algorithms and Theory of Computation Handbook, pp. 9.1\u20139.28, 2nd edn. CRC Press(2010). http:\/\/www.info.uniroma2.it\/~italiano\/Papers\/dyn-survey.ps.Z","key":"56_CR21"},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D., Goodrich, M.T., Korkmaz, D., Mamano, N.: Defining equitable geographic districts in road networks via stable matching. In: 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (2017)","key":"56_CR22","DOI":"10.1145\/3139958.3140015"},{"issue":"1\u20132","key":"56_CR23","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1142\/S0218195908002568","volume":"18","author":"D Eppstein","year":"2008","unstructured":"Eppstein, D., Goodrich, M.T., Sun, J.Z.: Skip quadtrees: dynamic data structures for multidimensional point sets. Int. J. Comput. Geom. Appl. 18(1\u20132), 131\u2013160 (2008)","journal-title":"Int. J. Comput. Geom. Appl."},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D., Goodrich, M.T., Trott, L.: Going off-road: transversal complexity in road networks. In: 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 23\u201332 (2009)","key":"56_CR24","DOI":"10.1145\/1653771.1653778"},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D., Gupta, S.: Crossing patterns in nonplanar road networks. In: 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, September 2017","key":"56_CR25","DOI":"10.1145\/3139958.3139999"},{"issue":"3","key":"56_CR26","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1002\/1097-0037(200010)36:3<156::AID-NET2>3.0.CO;2-L","volume":"36","author":"M Erwig","year":"2000","unstructured":"Erwig, M.: The graph Voronoi diagram with applications. Networks 36(3), 156\u2013163 (2000)","journal-title":"Networks"},{"doi-asserted-by":"crossref","unstructured":"Frieze, A.M., Miller, G.L., Teng, S.H.: Separator based parallel divide and conquer in computational geometry. In: 4th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 420\u2013429 (1992). http:\/\/doi.acm.org\/10.1145\/140901.141934","key":"56_CR27","DOI":"10.1145\/140901.141934"},{"issue":"1","key":"56_CR28","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/s004530010032","volume":"28","author":"D Frigioni","year":"2000","unstructured":"Frigioni, D., Italiano, G.F.: Dynamically switching vertices in planar graphs. Algorithmica 28(1), 76\u2013103 (2000)","journal-title":"Algorithmica"},{"issue":"3","key":"56_CR29","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/0196-6774(84)90019-1","volume":"5","author":"JR Gilbert","year":"1984","unstructured":"Gilbert, J.R., Hutchinson, J.P., Tarjan, R.E.: A separator theorem for graphs of bounded genus. J. Algorithms 5(3), 391\u2013407 (1984)","journal-title":"J. Algorithms"},{"issue":"3","key":"56_CR30","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1006\/jcss.1995.1076","volume":"51","author":"MT Goodrich","year":"1995","unstructured":"Goodrich, M.T.: Planar separators and parallel polygon triangulation. J. Comput. Syst. Sci. 51(3), 374\u2013389 (1995)","journal-title":"J. Comput. Syst. Sci."},{"key":"56_CR31","volume-title":"Algorithm Design and Applications","author":"MT Goodrich","year":"2014","unstructured":"Goodrich, M.T., Tamassia, R.: Algorithm Design and Applications, 1st edn. Wiley, Hoboken (2014)","edition":"1"},{"issue":"1","key":"56_CR32","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1006\/jcss.1997.1493","volume":"55","author":"MR Henzinger","year":"1997","unstructured":"Henzinger, M.R., Klein, P., Rao, S., Subramanian, S.: Faster shortest-path algorithms for planar graphs. J. Comput. Syst. Sci. 55(1), 3\u201323 (1997)","journal-title":"J. Comput. Syst. Sci."},{"doi-asserted-by":"crossref","unstructured":"Kaplan, H., Mulzer, W., Roditty, L., Seiferth, P., Sharir, M.: Dynamic planar Voronoi diagrams for general distance functions and their algorithmic applications. In: 28th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 2495\u20132504 (2017)","key":"56_CR33","DOI":"10.1137\/1.9781611974782.165"},{"doi-asserted-by":"crossref","unstructured":"Kawarabayashi, K., Reed, B.: A separator theorem in minor-closed classes. In: 51st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 153\u2013162 (2010)","key":"56_CR34","DOI":"10.1109\/FOCS.2010.22"},{"doi-asserted-by":"crossref","unstructured":"King, V.: Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In: 40th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 81\u201389 (1999)","key":"56_CR35","DOI":"10.1109\/SFFCS.1999.814580"},{"issue":"2","key":"56_CR36","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1137\/0136016","volume":"36","author":"RJ Lipton","year":"1979","unstructured":"Lipton, R.J., Tarjan, R.E.: A separator theorem for planar graphs. SIAM J. Appl. Math. 36(2), 177\u2013189 (1979)","journal-title":"SIAM J. Appl. Math."},{"issue":"2","key":"56_CR37","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s00453-010-9401-5","volume":"61","author":"L Roditty","year":"2011","unstructured":"Roditty, L., Zwick, U.: On dynamic shortest paths problems. Algorithmica 61(2), 389\u2013401 (2011)","journal-title":"Algorithmica"},{"key":"56_CR38","series-title":"Addison-Wesley Series in Computer Science","volume-title":"The design and analysis of spatial data structures","author":"H Samet","year":"1990","unstructured":"Samet, H.: The design and analysis of spatial data structures. Addison-Wesley Series in Computer Science. Addison-Wesley, Reading (1990)"}],"container-title":["Lecture Notes in Computer Science","LATIN 2018: Theoretical Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-77404-6_56","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T18:30:16Z","timestamp":1751481016000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-77404-6_56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319774039","9783319774046"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-77404-6_56","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"13 March 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"LATIN","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Latin American Symposium on Theoretical Informatics","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Buenos Aires","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Argentina","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 April 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 April 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"latin2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/latin2018.dc.uba.ar\/#","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}