{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:59:20Z","timestamp":1742914760230,"version":"3.40.3"},"publisher-location":"Cham","reference-count":43,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031099922"},{"type":"electronic","value":"9783031099939"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"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":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-09993-9_12","type":"book-chapter","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T20:12:42Z","timestamp":1656101562000},"page":"212-233","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributed Interactive Proofs for\u00a0the\u00a0Recognition of\u00a0Some Geometric Intersection Graph Classes"],"prefix":"10.1007","author":[{"given":"Benjamin","family":"Jauregui","sequence":"first","affiliation":[]},{"given":"Pedro","family":"Montealegre","sequence":"additional","affiliation":[]},{"given":"Ivan","family":"Rapaport","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,25]]},"reference":[{"issue":"2\u20134","key":"12_CR1","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.jda.2004.08.011","volume":"3","author":"MI Abouelhoda","year":"2005","unstructured":"Abouelhoda, M.I., Ohlebusch, E.: Chaining algorithms for multiple genome comparison. J. Discrete Algorithms 3(2\u20134), 321\u2013341 (2005)","journal-title":"J. Discrete Algorithms"},{"issue":"17","key":"12_CR2","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1016\/j.dam.2007.07.005","volume":"155","author":"K Asdre","year":"2007","unstructured":"Asdre, K., Ioannidou, K., Nikolopoulos, S.D.: The harmonious coloring problem is np-complete for interval and permutation graphs. Discrete Appl. Math. 155(17), 2377\u20132382 (2007)","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"12_CR3","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1016\/0022-0000(88)90028-1","volume":"36","author":"L Babai","year":"1988","unstructured":"Babai, L., Moran, S.: Arthur-merlin games: a randomized proof system, and a hierarchy of complexity classes. J. Comput. Syst. Sci. 36(2), 254\u2013276 (1988)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"12_CR4","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1145\/2402.322389","volume":"30","author":"C Beeri","year":"1983","unstructured":"Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. ACM (JACM) 30(3), 479\u2013513 (1983)","journal-title":"J. ACM (JACM)"},{"key":"12_CR5","doi-asserted-by":"crossref","unstructured":"Bousquet, N., Feuilloley, L., Pierron, T.: Local certification of graph decompositions and applications to minor-free classes. arXiv preprint arXiv:2108.00059 (2021)","DOI":"10.2139\/ssrn.4223289"},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Brandst\u00e4dt, A., Van Le, B., Spinrad, J.P.: Graph Classes: A Survey. Society for Industrial and Applied Mathematics, January 1999","DOI":"10.1137\/1.9780898719796"},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.tcs.2018.08.020","volume":"811","author":"K Censor-Hillel","year":"2020","unstructured":"Censor-Hillel, K., Paz, A., Perry, M.: Approximate proof-labeling schemes. Theoret. Comput. Sci. 811, 112\u2013124 (2020)","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"12_CR8","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/S0166-218X(98)00145-0","volume":"102","author":"HS Chao","year":"2000","unstructured":"Chao, H.S., Hsu, F.-R., Lee, R.C.T.: An optimal algorithm for finding the minimum cardinality dominating set on permutation graphs. Discrete Appl. Math. 102(3), 159\u2013173 (2000)","journal-title":"Discrete Appl. Math."},{"key":"12_CR9","unstructured":"Crescenzi, P., Fraigniaud, P., Paz, A.: Trade-offs in distributed interactive proofs. In: 33rd International Symposium on Distributed Computing (DISC 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)"},{"key":"12_CR10","doi-asserted-by":"crossref","unstructured":"Dagan, I., Golumbic, M.C., Pinter, R.Y.: Trapezoid graphs and their coloring. Discrete Appl. Math. 21(1), 35\u201346, 1988","DOI":"10.1016\/0166-218X(88)90032-7"},{"key":"12_CR11","doi-asserted-by":"crossref","unstructured":"Diestel, R.: Graph theory, 3rd ed. Graduate texts in mathematics, 173 (2005)","DOI":"10.1007\/978-3-642-14279-6_7"},{"key":"12_CR12","unstructured":"Feuilloley, L., Fraigniaud, P., Montealegre, P., Rapaport, I., R\u00e9mila, \u00c9., Todinca, I.: Local certification of graphs with bounded genus. arXiv preprint arXiv:2007.08084 (2020)"},{"key":"12_CR13","doi-asserted-by":"crossref","unstructured":"Feuilloley, L., Fraigniaud, P., Montealegre, P., Rapaport, I., R\u00e9mila, \u00c9., Todinca, I.: Compact distributed certification of planar graphs. Algorithmica, pp. 1\u201330 (2021)","DOI":"10.1145\/3382734.3404505"},{"key":"12_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1007\/978-3-030-24922-9_16","volume-title":"Structural Information and Communication Complexity","author":"P Fraigniaud","year":"2019","unstructured":"Fraigniaud, P., Montealegre, P., Oshman, R., Rapaport, I., Todinca, I.: On distributed Merlin-Arthur decision protocols. In: Censor-Hillel, K., Flammini, M. (eds.) SIROCCO 2019. LNCS, vol. 11639, pp. 230\u2013245. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-24922-9_16"},{"issue":"3","key":"12_CR15","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s00446-018-0340-8","volume":"32","author":"P Fraigniaud","year":"2019","unstructured":"Fraigniaud, P., Patt-Shamir, B., Perry, M.: Randomized proof-labeling schemes. Distrib. Comput. 32(3), 217\u2013234 (2019)","journal-title":"Distrib. Comput."},{"issue":"2","key":"12_CR16","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1137\/0601025","volume":"1","author":"MR Garey","year":"1980","unstructured":"Garey, M.R., Johnson, D.S., Miller, G.L., Papadimitriou, C.H.: The complexity of coloring circular arcs and chords. SIAM J. Algebraic Discrete Methods 1(2), 216\u2013227 (1980)","journal-title":"SIAM J. Algebraic Discrete Methods"},{"issue":"5\u20136","key":"12_CR17","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/S0020-0190(00)00025-9","volume":"73","author":"F Gavril","year":"2000","unstructured":"Gavril, F.: Maximum weight independent sets and cliques in intersection graphs of filaments. Inf. Process. Lett. 73(5\u20136), 181\u2013188 (2000)","journal-title":"Inf. Process. Lett."},{"issue":"3","key":"12_CR18","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1145\/116825.116852","volume":"38","author":"O Goldreich","year":"1991","unstructured":"Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in np have zero-knowledge proof systems. J. ACM (JACM) 38(3), 690\u2013728 (1991)","journal-title":"J. ACM (JACM)"},{"issue":"1","key":"12_CR19","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/0218012","volume":"18","author":"S Goldwasser","year":"1989","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186\u2013208 (1989)","journal-title":"SIAM J. Comput."},{"key":"12_CR20","doi-asserted-by":"crossref","unstructured":"Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Elsevier (2004)","DOI":"10.1016\/S0167-5060(04)80051-7"},{"issue":"1","key":"12_CR21","first-page":"1","volume":"12","author":"M G\u00f6\u00f6s","year":"2016","unstructured":"G\u00f6\u00f6s, M., Suomela, J.: Locally checkable proofs in distributed computing. Theory Comput. 12(1), 1\u201333 (2016)","journal-title":"Theory Comput."},{"key":"12_CR22","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.tcs.2018.11.028","volume":"811","author":"MM Halld\u00f3rsson","year":"2020","unstructured":"Halld\u00f3rsson, M.M., Konrad, C.: Improved distributed algorithms for coloring interval graphs with application to multicoloring trees. Theoretical Comput. Sci. 811, 29\u201341 (2020)","journal-title":"Theoretical Comput. Sci."},{"key":"12_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/978-3-642-45030-3_32","volume-title":"Algorithms and Computation","author":"MM Kant\u00e9","year":"2013","unstructured":"Kant\u00e9, M.M., Limouzy, V., Mary, A., Nourine, L., Uno, T.: On the enumeration and counting of minimal dominating sets in interval and permutation graphs. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) ISAAC 2013. LNCS, vol. 8283, pp. 339\u2013349. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-45030-3_32"},{"key":"12_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/11785293_7","volume-title":"Algorithm Theory \u2013 SWAT 2006","author":"H Kaplan","year":"2006","unstructured":"Kaplan, H., Nussbaum, Y.: A simpler linear-time recognition of circular-arc graphs. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 41\u201352. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11785293_7"},{"issue":"3","key":"12_CR25","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1137\/S0097539793258143","volume":"25","author":"H Kaplan","year":"1996","unstructured":"Kaplan, H., Shamir, R.: Pathwidth, bandwidth, and completion problems to proper interval graphs with small cliques. SIAM J. Comput. 25(3), 540\u2013561 (1996)","journal-title":"SIAM J. Comput."},{"key":"12_CR26","doi-asserted-by":"crossref","unstructured":"Ton Kloks. Treewidth of circle graphs. In International Symposium on Algorithms and Computation, pages 108\u2013117. Springer, 1993","DOI":"10.1007\/3-540-57568-5_240"},{"key":"12_CR27","doi-asserted-by":"crossref","unstructured":"Gillat Kol, Rotem Oshman, and Raghuvansh R Saxena. Interactive distributed proofs. In ACM Symposium on Principles of Distributed Computing, pages 255\u2013264. ACM, 2018","DOI":"10.1145\/3212734.3212771"},{"key":"12_CR28","unstructured":"Konrad, C., Zamaraev, V.: Distributed minimum vertex coloring and maximum independent set in chordal graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)"},{"issue":"4","key":"12_CR29","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s00446-010-0095-3","volume":"22","author":"A Korman","year":"2010","unstructured":"Korman, A., Kutten, S., Peleg, D.: Proof labeling schemes. Distrib. Comput. 22(4), 215\u2013233 (2010)","journal-title":"Distrib. Comput."},{"issue":"2","key":"12_CR30","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1137\/S0097539703437855","volume":"36","author":"D Kratsch","year":"2006","unstructured":"Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithms for recognizing interval graphs and permutation graphs. SIAM J. Comput. 36(2), 326\u2013353 (2006)","journal-title":"SIAM J. Comput."},{"issue":"3","key":"12_CR31","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1016\/j.ejc.2011.10.011","volume":"34","author":"E Lappas","year":"2013","unstructured":"Lappas, E., Nikolopoulos, S.D., Palios, L.: An o (n)-time algorithm for the paired domination problem on permutation graphs. Eur. J. Combinatorics 34(3), 593\u2013608 (2013)","journal-title":"Eur. J. Combinatorics"},{"issue":"4","key":"12_CR32","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1145\/146585.146605","volume":"39","author":"C Lund","year":"1992","unstructured":"Lund, C., Fortnow, L., Karloff, H., Nisan, N.: Algebraic methods for interactive proof systems. J. ACM (JACM) 39(4), 859\u2013868 (1992)","journal-title":"J. ACM (JACM)"},{"issue":"2","key":"12_CR33","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1006\/jagm.1994.1034","volume":"17","author":"T-H Ma","year":"1994","unstructured":"Ma, T.-H., Spinrad, J.P.: On the 2-chain subgraph cover and related problems. J. Algorithms 17(2), 251\u2013268 (1994)","journal-title":"J. Algorithms"},{"issue":"2","key":"12_CR34","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s00453-003-1032-7","volume":"37","author":"RM McConnell","year":"2003","unstructured":"McConnell, R.M.: Linear-time recognition of circular-arc graphs. Algorithmica 37(2), 93\u2013147 (2003)","journal-title":"Algorithmica"},{"key":"12_CR35","doi-asserted-by":"publisher","unstructured":"McKee, T.A., McMorris, F.R.: Topics in Intersection Graph Theory. Society for Industrial and Applied Mathematics, January 1999. https:\/\/doi.org\/10.1137\/1.9780898719802","DOI":"10.1137\/1.9780898719802"},{"key":"12_CR36","unstructured":"Montealegre, P., Ram\u00edrez-Romero, D., Rapaport, I.: Shared vs private randomness in distributed interactive proofs. LIPIcs, vol. 181, pp. 51:1\u201351:13. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2020)"},{"key":"12_CR37","doi-asserted-by":"crossref","unstructured":"Naor, M., Parter, M., Yogev, E.: The power of distributed verifiers in interactive proofs. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1096\u2013115. SIAM (2020)","DOI":"10.1137\/1.9781611975994.67"},{"issue":"6","key":"12_CR38","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1137\/S0097539793254571","volume":"24","author":"M Naor","year":"1995","unstructured":"Naor, M., Stockmeyer, L.: What can be computed locally? SIAM J. Comput. 24(6), 1259\u20131277 (1995)","journal-title":"SIAM J. Comput."},{"key":"12_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/978-3-540-74839-7_23","volume-title":"Graph-Theoretic Concepts in Computer Science","author":"M Pergel","year":"2007","unstructured":"Pergel, M.: Recognition of Polygon-Circle Graphs and Graphs of Interval Filaments Is NP-Complete. In: Brandst\u00e4dt, A., Kratsch, D., M\u00fcller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 238\u2013247. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-74839-7_23"},{"issue":"4","key":"12_CR40","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1145\/146585.146609","volume":"39","author":"A Shamir","year":"1992","unstructured":"Shamir, A.: Ip= pspace. J. ACM (JACM) 39(4), 869\u2013877 (1992)","journal-title":"J. ACM (JACM)"},{"issue":"2","key":"12_CR41","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1006\/jagm.1994.1012","volume":"16","author":"J Spinrad","year":"1994","unstructured":"Spinrad, J.: Recognition of circle graphs. J. Algorithms 16(2), 264\u2013282 (1994)","journal-title":"J. Algorithms"},{"issue":"4","key":"12_CR42","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1007\/s00453-013-9830-z","volume":"71","author":"A Tiskin","year":"2015","unstructured":"Tiskin, A.: Fast distance multiplication of unit-monge matrices. Algorithmica 71(4), 859\u2013888 (2015)","journal-title":"Algorithmica"},{"key":"12_CR43","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.tcs.2019.04.017","volume":"806","author":"K Yamazaki","year":"2020","unstructured":"Yamazaki, K., Saitoh, T., Kiyomi, M., Uehara, R.: Enumeration of nonisomorphic interval graphs and nonisomorphic permutation graphs. Theoret. Comput. Sci. 806, 310\u2013322 (2020)","journal-title":"Theoret. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Structural Information and Communication Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-09993-9_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T19:27:40Z","timestamp":1727465260000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-09993-9_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031099922","9783031099939"],"references-count":43,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-09993-9_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"25 June 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SIROCCO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Colloquium on Structural Information and Communication Complexity","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paderborn","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 June 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 June 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sirocco2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sirocco2022.cs.uni-paderborn.de\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}