Marcel Jackiewicz, Adam Kasperski, Paweł Zieliński
{"title":"具有离散追索权的可恢复稳健最短路径问题的计算复杂性","authors":"Marcel Jackiewicz, Adam Kasperski, Paweł Zieliński","doi":"arxiv-2403.20000","DOIUrl":null,"url":null,"abstract":"In this paper the recoverable robust shortest path problem is investigated.\nDiscrete budgeted interval uncertainty representation is used to model\nuncertain second-stage arc costs. The known complexity results for this problem\nare strengthened. It is shown that it is Sigma_3^p-hard for the arc exclusion\nand the arc symmetric difference neighborhoods. Furthermore, it is also proven\nthat the inner adversarial problem for these neighborhoods is Pi_2^p-hard.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse\",\"authors\":\"Marcel Jackiewicz, Adam Kasperski, Paweł Zieliński\",\"doi\":\"arxiv-2403.20000\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper the recoverable robust shortest path problem is investigated.\\nDiscrete budgeted interval uncertainty representation is used to model\\nuncertain second-stage arc costs. The known complexity results for this problem\\nare strengthened. It is shown that it is Sigma_3^p-hard for the arc exclusion\\nand the arc symmetric difference neighborhoods. Furthermore, it is also proven\\nthat the inner adversarial problem for these neighborhoods is Pi_2^p-hard.\",\"PeriodicalId\":501024,\"journal\":{\"name\":\"arXiv - CS - Computational Complexity\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.20000\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.20000","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse
In this paper the recoverable robust shortest path problem is investigated.
Discrete budgeted interval uncertainty representation is used to model
uncertain second-stage arc costs. The known complexity results for this problem
are strengthened. It is shown that it is Sigma_3^p-hard for the arc exclusion
and the arc symmetric difference neighborhoods. Furthermore, it is also proven
that the inner adversarial problem for these neighborhoods is Pi_2^p-hard.