{"title":"一种快速参数化共径集算法","authors":"Blair D. Sullivan, Andrew van der Poel","doi":"10.4230/LIPIcs.IPEC.2016.28","DOIUrl":null,"url":null,"abstract":"The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.","PeriodicalId":137775,"journal":{"name":"International Symposium on Parameterized and Exact Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Fast Parameterized Algorithm for Co-Path Set\",\"authors\":\"Blair D. Sullivan, Andrew van der Poel\",\"doi\":\"10.4230/LIPIcs.IPEC.2016.28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.\",\"PeriodicalId\":137775,\"journal\":{\"name\":\"International Symposium on Parameterized and Exact Computation\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Parameterized and Exact Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.IPEC.2016.28\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Parameterized and Exact Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.IPEC.2016.28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
k- co - path SET问题的问题是，给定一个图G和一个正整数k，是否可以从G中删除k条边，使余数是不相交路径的集合。我们给出了一种复杂度为O^*(1.588^k)的线性时间fpt算法来决定k- co - path SET，显著改善了Feng、Zhou和Wang(2015)之前最著名的O^*(2.17^k)算法。我们的主要工具是一个新的O^*(4^{tw(G)})算法，用于使用Cut&Count框架的CO-PATH SET，其中tw(G)表示树宽。在一般图中，我们将其与分支算法相结合，该算法将6k内核细化为简化实例，我们证明了这些实例具有有限的树宽。
The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.
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