Ernst Althaus, Dan Schnurbusch, Julian Wüschner, Sarah Ziegler
{"title":"计算树宽度的Tamaki算法","authors":"Ernst Althaus, Dan Schnurbusch, Julian Wüschner, Sarah Ziegler","doi":"10.4230/LIPIcs.SEA.2021.9","DOIUrl":null,"url":null,"abstract":"We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"1 1","pages":"9:1-9:18"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On Tamaki's Algorithm to Compute Treewidths\",\"authors\":\"Ernst Althaus, Dan Schnurbusch, Julian Wüschner, Sarah Ziegler\",\"doi\":\"10.4230/LIPIcs.SEA.2021.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability\",\"PeriodicalId\":9448,\"journal\":{\"name\":\"Bulletin of the Society of Sea Water Science, Japan\",\"volume\":\"1 1\",\"pages\":\"9:1-9:18\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Society of Sea Water Science, Japan\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.SEA.2021.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Society of Sea Water Science, Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.SEA.2021.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability
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