Nathann Cohen, Mathieu Hilaire, Nícolas A. Martins, N. Nisse, S. Pérennes
{"title":"Spy-Game on Graphs","authors":"Nathann Cohen, Mathieu Hilaire, Nícolas A. Martins, N. Nisse, S. Pérennes","doi":"10.4230/LIPIcs.FUN.2016.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.FUN.2016.10","url":null,"abstract":"We define and study the following two-player game on a graph G. Let k in N^*. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s in N^* is his speed. Then, each guard may move along one edge. The spy and the guards may occupy same vertices. The spy has to escape the surveillance of the guards, i.e., must reach a vertex at distance more than d in N (a predefined distance) from every guard. Can the spy win against k guards? Similarly, what is the minimum distance d such that k guards may ensure that at least one of them remains at distance at most d from the spy? \u0000This game generalizes two well-studied games: Cops and robber games (when s=1) and Eternal Dominating Set (when s is unbounded). \u0000 \u0000We consider the computational complexity of the problem, showing that it is NP-hard and that it is PSPACE-hard in DAGs. Then, we establish tight tradeoffs between the number of guards and the required distance d when G is a path or a cycle. Our main result is that there exists beta>0 such that Omega(n^{1+beta}) guards are required to win in any n*n grid.","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122997347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximability of Latin Square Completion-Type Puzzles","authors":"Kazuya Haraguchi, H. Ono","doi":"10.1007/978-3-319-07890-8_19","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_19","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129305199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"UNO Gets Easier for a Single Player","authors":"P. Dey, Prachi Goyal, Neeldhara Misra","doi":"10.1007/978-3-319-07890-8_13","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_13","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129300325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algorithmic Gems in the Data Miner's Cave","authors":"P. Boldi","doi":"10.1007/978-3-319-07890-8_1","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_1","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123850090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Another Look at the Shoelace TSP: The Case of Very Old Shoes","authors":"V. Deineko, G. Woeginger","doi":"10.1007/978-3-319-07890-8_11","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_11","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125904457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michele Borassi, P. Crescenzi, M. Habib, W. Kosters, Andrea Marino, Frank W. Takes
{"title":"On the Solvability of the Six Degrees of Kevin Bacon Game - A Faster Graph Diameter and Radius Computation Method","authors":"Michele Borassi, P. Crescenzi, M. Habib, W. Kosters, Andrea Marino, Frank W. Takes","doi":"10.1007/978-3-319-07890-8_5","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_5","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124391990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Synchronized Dancing of Oblivious Chameleons","authors":"S. Das, P. Flocchini, G. Prencipe, N. Santoro","doi":"10.1007/978-3-319-07890-8_10","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_10","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115107619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How Even Tiny Influence Can Have a Big Impact!","authors":"Barbara Keller, D. Peleg, Roger Wattenhofer","doi":"10.1007/978-3-319-07890-8_22","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_22","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128371964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Being Negative Makes Life NP-hard (for Product Sellers)","authors":"S. O. Krumke, Florian D. Schwahn, Clemens Thielen","doi":"10.1007/978-3-319-07890-8_24","DOIUrl":"https://doi.org/10.1007/978-3-319-07890-8_24","url":null,"abstract":"","PeriodicalId":293763,"journal":{"name":"Fun with Algorithms","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133277516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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