{"date_updated":"2023-07-25T11:48:36Z","year":"2002","publication":"Proceedings of the 13th International Symposium on Algorithms and Computation","date_created":"2018-12-11T11:57:34Z","abstract":[{"text":"Intersection graphs of disks and of line segments, respectively, have been well studied, because of both, practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses which in a sense, interpolate between disc and ellipses, and show that it is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounded.","lang":"eng"}],"citation":{"ieee":"C. Ambühl and U. Wagner, “On the Clique problem in intersection graphs of ellipses,” in <i>Proceedings of the 13th International Symposium on Algorithms and Computation</i>, Vancouver, Canada, 2002, vol. 2518, pp. 489–500.","chicago":"Ambühl, Christoph, and Uli Wagner. “On the Clique Problem in Intersection Graphs of Ellipses.” In <i>Proceedings of the 13th International Symposium on Algorithms and Computation</i>, 2518:489–500. Springer, 2002. <a href=\"https://doi.org/10.1007/3-540-36136-7_43\">https://doi.org/10.1007/3-540-36136-7_43</a>.","apa":"Ambühl, C., &#38; Wagner, U. (2002). On the Clique problem in intersection graphs of ellipses. In <i>Proceedings of the 13th International Symposium on Algorithms and Computation</i> (Vol. 2518, pp. 489–500). Vancouver, Canada: Springer. <a href=\"https://doi.org/10.1007/3-540-36136-7_43\">https://doi.org/10.1007/3-540-36136-7_43</a>","ama":"Ambühl C, Wagner U. On the Clique problem in intersection graphs of ellipses. In: <i>Proceedings of the 13th International Symposium on Algorithms and Computation</i>. Vol 2518. Springer; 2002:489-500. doi:<a href=\"https://doi.org/10.1007/3-540-36136-7_43\">10.1007/3-540-36136-7_43</a>","short":"C. Ambühl, U. Wagner, in:, Proceedings of the 13th International Symposium on Algorithms and Computation, Springer, 2002, pp. 489–500.","ista":"Ambühl C, Wagner U. 2002. On the Clique problem in intersection graphs of ellipses. Proceedings of the 13th International Symposium on Algorithms and Computation. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 2518, 489–500.","mla":"Ambühl, Christoph, and Uli Wagner. “On the Clique Problem in Intersection Graphs of Ellipses.” <i>Proceedings of the 13th International Symposium on Algorithms and Computation</i>, vol. 2518, Springer, 2002, pp. 489–500, doi:<a href=\"https://doi.org/10.1007/3-540-36136-7_43\">10.1007/3-540-36136-7_43</a>."},"type":"conference","publication_identifier":{"isbn":["9783540001423"]},"conference":{"start_date":"2002-11-21","name":"ISAAC: International Symposium on Algorithms and Computation","end_date":"2002-11-23","location":"Vancouver, Canada"},"month":"01","article_processing_charge":"No","intvolume":"      2518","language":[{"iso":"eng"}],"scopus_import":"1","date_published":"2002-01-01T00:00:00Z","day":"01","status":"public","author":[{"first_name":"Christoph","last_name":"Ambühl","full_name":"Ambühl, Christoph"},{"last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli"}],"oa_version":"None","doi":"10.1007/3-540-36136-7_43","quality_controlled":"1","_id":"2421","volume":2518,"page":"489 - 500","publisher":"Springer","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","extern":"1","publist_id":"4504","title":"On the Clique problem in intersection graphs of ellipses","alternative_title":["LNCS"]}