{"title":"强连通有向图上MAPF的小解假设成立","authors":"B. Nebel","doi":"10.1609/icaps.v33i1.27208","DOIUrl":null,"url":null,"abstract":"The determination of the computational complexity of multi-agent pathfinding on directed graphs (diMAPF) has been an open research problem for many years. While diMAPF has been shown to be polynomial for some special cases, only recently, it has been established that the problem is NP-hard in general. Further, it has been proved that diMAPF will be in NP if the short solution hypothesis for strongly connected directed graphs holds. In this paper, it is shown that this hypothesis is indeed true, even when one allows for synchronous rotations.","PeriodicalId":239898,"journal":{"name":"International Conference on Automated Planning and Scheduling","volume":"22 4","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Small Solution Hypothesis for MAPF on Strongly Connected Directed Graphs Is True\",\"authors\":\"B. Nebel\",\"doi\":\"10.1609/icaps.v33i1.27208\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The determination of the computational complexity of multi-agent pathfinding on directed graphs (diMAPF) has been an open research problem for many years. While diMAPF has been shown to be polynomial for some special cases, only recently, it has been established that the problem is NP-hard in general. Further, it has been proved that diMAPF will be in NP if the short solution hypothesis for strongly connected directed graphs holds. In this paper, it is shown that this hypothesis is indeed true, even when one allows for synchronous rotations.\",\"PeriodicalId\":239898,\"journal\":{\"name\":\"International Conference on Automated Planning and Scheduling\",\"volume\":\"22 4\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Conference on Automated Planning and Scheduling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1609/icaps.v33i1.27208\",\"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 Conference on Automated Planning and Scheduling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1609/icaps.v33i1.27208","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Small Solution Hypothesis for MAPF on Strongly Connected Directed Graphs Is True
The determination of the computational complexity of multi-agent pathfinding on directed graphs (diMAPF) has been an open research problem for many years. While diMAPF has been shown to be polynomial for some special cases, only recently, it has been established that the problem is NP-hard in general. Further, it has been proved that diMAPF will be in NP if the short solution hypothesis for strongly connected directed graphs holds. In this paper, it is shown that this hypothesis is indeed true, even when one allows for synchronous rotations.
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