{"title":"图问题的完美紧致对称破缺","authors":"Marijn J. H. Heule","doi":"10.1109/SYNASC.2016.034","DOIUrl":null,"url":null,"abstract":"Symmetry breaking is a crucial technique to solve many graph problems. However, current state-of-the-art techniques break graph symmetries only partially, causing search algorithms to unnecessarily explore many isomorphic parts of the search space. We study properties of perfect symmetry breaking for graph problems. One promising and surprising result on small-sized graphs—up to order five— is that perfect symmetry breaking can be achieved using a compact propositional formula in which each literal occurs at most twice. At least for small graphs, perfect symmetry breaking can be expressed more compactly than the existing (partial) symmetry-breaking methods. We present several techniques to compute and analyze perfect symmetry-breaking formulas.","PeriodicalId":268635,"journal":{"name":"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The Quest for Perfect and Compact Symmetry Breaking for Graph Problems\",\"authors\":\"Marijn J. H. Heule\",\"doi\":\"10.1109/SYNASC.2016.034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Symmetry breaking is a crucial technique to solve many graph problems. However, current state-of-the-art techniques break graph symmetries only partially, causing search algorithms to unnecessarily explore many isomorphic parts of the search space. We study properties of perfect symmetry breaking for graph problems. One promising and surprising result on small-sized graphs—up to order five— is that perfect symmetry breaking can be achieved using a compact propositional formula in which each literal occurs at most twice. At least for small graphs, perfect symmetry breaking can be expressed more compactly than the existing (partial) symmetry-breaking methods. We present several techniques to compute and analyze perfect symmetry-breaking formulas.\",\"PeriodicalId\":268635,\"journal\":{\"name\":\"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2016.034\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2016.034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Quest for Perfect and Compact Symmetry Breaking for Graph Problems
Symmetry breaking is a crucial technique to solve many graph problems. However, current state-of-the-art techniques break graph symmetries only partially, causing search algorithms to unnecessarily explore many isomorphic parts of the search space. We study properties of perfect symmetry breaking for graph problems. One promising and surprising result on small-sized graphs—up to order five— is that perfect symmetry breaking can be achieved using a compact propositional formula in which each literal occurs at most twice. At least for small graphs, perfect symmetry breaking can be expressed more compactly than the existing (partial) symmetry-breaking methods. We present several techniques to compute and analyze perfect symmetry-breaking formulas.
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