{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T18:37:01Z","timestamp":1770921421617,"version":"3.50.1"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032178008","type":"print"},{"value":"9783032178015","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-17801-5_38","type":"book-chapter","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:53:31Z","timestamp":1770918811000},"page":"517-531","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hypergraphs as\u00a0Metro Maps: Drawing Paths with\u00a0Few Bends in\u00a0Trees, Cacti, and\u00a0Plane 4-Graphs"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1688-394X","authenticated-orcid":false,"given":"Sabine","family":"Cornelsen","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1441-4189","authenticated-orcid":false,"given":"Henry","family":"F\u00f6rster","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4671-9822","authenticated-orcid":false,"given":"Siddharth","family":"Gupta","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0477-2724","authenticated-orcid":false,"given":"Stephen","family":"Kobourov","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7398-718X","authenticated-orcid":false,"given":"Johannes","family":"Zink","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"38_CR1","doi-asserted-by":"publisher","unstructured":"Alsallakh, B., Micallef, L., Aigner, W., Hauser, H., Miksch, S., Rodgers, P.J.: The state-of-the-art of set visualization. Comput. Graph. Forum 35(1), 234\u2013260 (2016). https:\/\/doi.org\/10.1111\/cgf.12722","DOI":"10.1111\/cgf.12722"},{"issue":"3","key":"38_CR2","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1111\/CGF.13986","volume":"39","author":"H Bast","year":"2020","unstructured":"Bast, H., Brosi, P., Storandt, S.: Metro maps on octilinear grid graphs. Comput. Graph. Forum 39(3), 357\u2013367 (2020). https:\/\/doi.org\/10.1111\/CGF.13986","journal-title":"Comput. Graph. Forum"},{"key":"38_CR3","doi-asserted-by":"publisher","unstructured":"Bast, H., Brosi, P., Storandt, S.: Metro maps on flexible base grids. In: Hoel, E., Oliver, D., Wong, R.C., Eldawy, A. (eds.) Proceedings of the 17th International Symposium on Spatial and Temporal Databases, SSTD 2021, pp. 12\u201322. ACM (2021). https:\/\/doi.org\/10.1145\/3469830.3470899","DOI":"10.1145\/3469830.3470899"},{"issue":"6","key":"38_CR4","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1111\/CGF.14497","volume":"41","author":"MA Bekos","year":"2022","unstructured":"Bekos, M.A., et al.: Computing schematic layouts for spatial hypergraphs on concentric circles and grids. Comput. Graph. Forum 41(6), 316\u2013335 (2022). https:\/\/doi.org\/10.1111\/CGF.14497","journal-title":"Comput. Graph. Forum"},{"key":"38_CR5","doi-asserted-by":"publisher","unstructured":"van\u00a0den Brand, J., et al.: A deterministic almost-linear time algorithm for minimum-cost flow. In: Proceedings of the 64th Annual Symposium on Foundations of Computer Science, FOCS 2023, pp. 503\u2013514. IEEE (2023). https:\/\/doi.org\/10.1109\/FOCS57990.2023.00037","DOI":"10.1109\/FOCS57990.2023.00037"},{"key":"38_CR6","doi-asserted-by":"publisher","unstructured":"Brandes, U., Cornelsen, S., Pampel, B., Sallaberry, A.: Blocks of hypergraphs - applied to hypergraphs and outerplanarity. In: Iliopoulos, C.S., Smyth, W.F. (eds.) Proceedings of the 21st International Workshop on Combinatorial Algorithms, IWOCA 2010. Lecture Notes in Computer Science, vol.\u00a06460, pp. 201\u2013211. Springer (2010). https:\/\/doi.org\/10.1007\/978-3-642-19222-7_21","DOI":"10.1007\/978-3-642-19222-7_21"},{"key":"38_CR7","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/J.JDA.2011.12.009","volume":"14","author":"U Brandes","year":"2012","unstructured":"Brandes, U., Cornelsen, S., Pampel, B., Sallaberry, A.: Path-based supports for hypergraphs. J. Discrete Algorithms 14, 248\u2013261 (2012). https:\/\/doi.org\/10.1016\/J.JDA.2011.12.009","journal-title":"J. Discrete Algorithms"},{"issue":"4","key":"38_CR8","doi-asserted-by":"publisher","first-page":"533","DOI":"10.7155\/JGAA.00237","volume":"15","author":"K Buchin","year":"2011","unstructured":"Buchin, K., van Kreveld, M.J., Meijer, H., Speckmann, B., Verbeek, K.: On planar supports for hypergraphs. J. Graph Algorithms Appl. 15(4), 533\u2013549 (2011). https:\/\/doi.org\/10.7155\/JGAA.00237","journal-title":"J. Graph Algorithms Appl."},{"issue":"3","key":"38_CR9","doi-asserted-by":"publisher","first-page":"463","DOI":"10.7155\/JGAA.00499","volume":"23","author":"T Castermans","year":"2019","unstructured":"Castermans, T., van Garderen, M., Meulemans, W., N\u00f6llenburg, M., Yuan, X.: Short plane supports for spatial hypergraphs. J. Graph Algorithms Appl. 23(3), 463\u2013498 (2019). https:\/\/doi.org\/10.7155\/JGAA.00499","journal-title":"J. Graph Algorithms Appl."},{"key":"38_CR10","unstructured":"Cornelsen, S., F\u00f6rster, H., Gupta, S., Kobourov, S., Zink, J.: Hypergraphs as metro maps: drawing paths with few bends in trees, cacti, and plane 4-graphs. arXiv report (2025). http:\/\/arxiv.org\/abs\/2511.22508"},{"key":"38_CR11","unstructured":"Dinitz, E.A., Karzanov, A.V., Lomonosov, M.V.: On the structure of a family of minimal weighted cuts in a graph. In: Fridman, A.A. (ed.) Studies in Discrete Optimization, Nauka, pp. 290\u2013306 (1976). in Russian"},{"key":"38_CR12","doi-asserted-by":"publisher","unstructured":"Dobler, A., Kobourov, S.G., Mondal, D., N\u00f6llenburg, M.: Representing hypergraphs by point-line incidences. In: Kr\u00e1lovic, R., Kurkov\u00e1, V. (eds.) Proceedings of the 50th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2025. Lecture Notes in Computer Science, vol. 15538, pp. 241\u2013254. Springer (2025). https:\/\/doi.org\/10.1007\/978-3-031-82670-2_18","DOI":"10.1007\/978-3-031-82670-2_18"},{"key":"38_CR13","doi-asserted-by":"publisher","unstructured":"Fink, M., et al.: Drawing metro maps using B\u00e9zier curves. In: Didimo, W., Patrignani, M. (eds.) Proceedings of the 20th International Symposium on Graph Drawing, GD 2012. Lecture Notes in Computer Science, vol.\u00a07704, pp. 463\u2013474. Springer (2012). https:\/\/doi.org\/10.1007\/978-3-642-36763-2_41","DOI":"10.1007\/978-3-642-36763-2_41"},{"key":"38_CR14","doi-asserted-by":"publisher","unstructured":"Fischer, M.T., Frings, A., Keim, D.A., Seebacher, D.: Towards a survey on static and dynamic hypergraph visualizations. In: Proceedings of 2021 IEEE Visualization Conference, VIS, pp. 81\u201385. IEEE (2021). https:\/\/doi.org\/10.1109\/VIS49827.2021.9623305","DOI":"10.1109\/VIS49827.2021.9623305"},{"key":"38_CR15","doi-asserted-by":"publisher","unstructured":"Frank, F., et al.: Using the metro-map metaphor for drawing hypergraphs. In: Bure\u0161, T., et al., (eds.) Proceedings of the 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021. LNCS, vol. 12607, pp. 361\u2013372. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-67731-2_26","DOI":"10.1007\/978-3-030-67731-2_26"},{"key":"38_CR16","doi-asserted-by":"publisher","unstructured":"Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for general graph-matching problems. J. ACM 38(4), 815\u2013853 (1991). https:\/\/doi.org\/10.1145\/115234.115366","DOI":"10.1145\/115234.115366"},{"key":"38_CR17","unstructured":"Hong, S., Merrick, D., do\u00a0Nascimento, H.A.D.: The metro map layout problem. In: Churcher, N., Churcher, C. (eds.) Proceedings of the Australasian Symposium on Information Visualisation, InVis.au 2004. CRPIT, vol.\u00a035, pp. 91\u2013100. Australian Computer Society (2004). http:\/\/crpit.scem.westernsydney.edu.au\/abstracts\/CRPITV35Hong.html"},{"issue":"2","key":"38_CR18","doi-asserted-by":"publisher","first-page":"1257","DOI":"10.1109\/TVCG.2020.3030475","volume":"27","author":"B Jacobsen","year":"2021","unstructured":"Jacobsen, B., Wallinger, M., Kobourov, S., N\u00f6llenburg, M.: Metrosets: Visualizing sets as metro maps. IEEE Trans. Visual Comput. Graphics 27(2), 1257\u20131267 (2021). https:\/\/doi.org\/10.1109\/TVCG.2020.3030475","journal-title":"IEEE Trans. Visual Comput. Graphics"},{"issue":"3","key":"38_CR19","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1002\/JGT.3190110306","volume":"11","author":"DS Johnson","year":"1987","unstructured":"Johnson, D.S., Pollak, H.O.: Hypergraph planarity and the complexity of drawing Venn diagrams. J. Graph Theory 11(3), 309\u2013325 (1987). https:\/\/doi.org\/10.1002\/JGT.3190110306","journal-title":"J. Graph Theory"},{"key":"38_CR20","doi-asserted-by":"publisher","unstructured":"Kaufmann, M., van Kreveld, M.J., Speckmann, B.: Subdivision drawings of hypergraphs. In: Tollis, I.G., Patrignani, M. (eds.) Proceedings of the 16th International Symposium on Graph Drawing, GD 2008. Lecture Notes in Computer Science, vol.\u00a05417, pp. 396\u2013407. Springer (2008). https:\/\/doi.org\/10.1007\/978-3-642-00219-9_39","DOI":"10.1007\/978-3-642-00219-9_39"},{"key":"38_CR21","doi-asserted-by":"publisher","unstructured":"Klemz, B., Mchedlidze, T., N\u00f6llenburg, M.: Minimum tree supports for hypergraphs and low-concurrency Euler diagrams. In: Ravi, R., G\u00f8rtz, I.L. (eds.) Proceedings of the 14th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2014. LNCS, vol. 8503, pp. 265\u2013276. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-08404-6_23","DOI":"10.1007\/978-3-319-08404-6_23"},{"key":"38_CR22","doi-asserted-by":"publisher","unstructured":"Nickel, S., N\u00f6llenburg, M.: Towards data-driven multilinear metro maps. In: Pietarinen, A., et al., (eds.) Proceedings of the 11th International Conference on Diagrammatic Representation and Inference, Diagrams 2020. Lecture Notes in Computer Science, vol. 12169, pp. 153\u2013161. Springer (2020). https:\/\/doi.org\/10.1007\/978-3-030-54249-8_12","DOI":"10.1007\/978-3-030-54249-8_12"},{"issue":"5","key":"38_CR23","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1109\/TVCG.2010.81","volume":"17","author":"M N\u00f6llenburg","year":"2011","unstructured":"N\u00f6llenburg, M., Wolff, A.: Drawing and labeling high-quality metro maps by mixed-integer programming. IEEE Trans. Visual Comput. Graphics 17(5), 626\u2013641 (2011). https:\/\/doi.org\/10.1109\/TVCG.2010.81","journal-title":"IEEE Trans. Visual Comput. Graphics"},{"key":"38_CR24","doi-asserted-by":"publisher","unstructured":"Schaefer, M.: Complexity of some geometric and topological problems. In: Eppstein, D., Gansner, E.R. (eds.) Proceedings of the 17th International Symposium of Graph Drawing, GD 2009. Lecture Notes in Computer Science, vol.\u00a05849, pp. 334\u2013344. Springer (2009). https:\/\/doi.org\/10.1007\/978-3-642-11805-0_32","DOI":"10.1007\/978-3-642-11805-0_32"},{"issue":"2","key":"38_CR25","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1137\/S0097539792235487","volume":"23","author":"R Swaminathan","year":"1994","unstructured":"Swaminathan, R., Wagner, D.K.: On the consecutive-retrieval problem. SIAM J. Comput. 23(2), 398\u2013414 (1994). https:\/\/doi.org\/10.1137\/S0097539792235487","journal-title":"SIAM J. Comput."},{"key":"38_CR26","doi-asserted-by":"publisher","unstructured":"Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16(3) (1987).https:\/\/doi.org\/10.1137\/0216030","DOI":"10.1137\/0216030"}],"container-title":["Lecture Notes in Computer Science","SOFSEM 2026: Theory and Practice of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-17801-5_38","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:53:33Z","timestamp":1770918813000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-17801-5_38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032178008","9783032178015"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-17801-5_38","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"13 February 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"SOFSEM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Current Trends in Theory and Practice of Computer Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Krakow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 February 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 February 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"51","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sofsem2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sofsem.uj.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}