{"title":"排列图中最大诱导匹配问题的动态规划算法","authors":"V. Nguyen, B. Pham, Viet-Hung Tran, Phan-Thuan Do","doi":"10.1145/3287921.3287961","DOIUrl":null,"url":null,"abstract":"For a finite undirected graph G = (V, E) and a positive integer k ≥ 1, an edge set M ⊆ E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been studied under the name maximum induced matching (MIM for short), i.e., a maximum matching which forms an induced subgraph in G. MIM arises in many applications, such as artificial intelligence, game theory, computer networks, VLSI design and marriage problems. In this paper, we design an O(n2) solution for finding MIM in permutation graphs based on a dynamic programming method on edges with the aid of the sweep line technique. Our result is better than the best known algorithm.","PeriodicalId":448008,"journal":{"name":"Proceedings of the 9th International Symposium on Information and Communication Technology","volume":"42 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A dynamic programming algorithm for the maximum induced matching problem in permutation graphs\",\"authors\":\"V. Nguyen, B. Pham, Viet-Hung Tran, Phan-Thuan Do\",\"doi\":\"10.1145/3287921.3287961\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a finite undirected graph G = (V, E) and a positive integer k ≥ 1, an edge set M ⊆ E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been studied under the name maximum induced matching (MIM for short), i.e., a maximum matching which forms an induced subgraph in G. MIM arises in many applications, such as artificial intelligence, game theory, computer networks, VLSI design and marriage problems. In this paper, we design an O(n2) solution for finding MIM in permutation graphs based on a dynamic programming method on edges with the aid of the sweep line technique. Our result is better than the best known algorithm.\",\"PeriodicalId\":448008,\"journal\":{\"name\":\"Proceedings of the 9th International Symposium on Information and Communication Technology\",\"volume\":\"42 6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 9th International Symposium on Information and Communication Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3287921.3287961\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 9th International Symposium on Information and Communication Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3287921.3287961","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A dynamic programming algorithm for the maximum induced matching problem in permutation graphs
For a finite undirected graph G = (V, E) and a positive integer k ≥ 1, an edge set M ⊆ E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been studied under the name maximum induced matching (MIM for short), i.e., a maximum matching which forms an induced subgraph in G. MIM arises in many applications, such as artificial intelligence, game theory, computer networks, VLSI design and marriage problems. In this paper, we design an O(n2) solution for finding MIM in permutation graphs based on a dynamic programming method on edges with the aid of the sweep line technique. Our result is better than the best known algorithm.