Shiri, D. orcid.org/0000-0003-2884-0047 and Tozan, H. (2022) Online routing and searching on graphs with blocked edges. Journal of Combinatorial Optimization, 44 (2). pp. 1039-1059. ISSN 1382-6905
Abstract
We study routing and searching decisions of a search-and-detection (SDT) team on a road network under online uncertainty setting. Given an undirected edge-weighted bounded graph, a static target is positioned at an unknown vertex among potential target vertices in the graph. A non-negative search cost is given on each of the potential target vertices. The target is detected once the SDT searches its corresponding vertex. There may be some non-recoverable online blockages in the graph, but the existence of blockages is unknown to the SDT initially. If a blockage exists in the graph, it is disclosed online once the SDT visits one of its end-vertices. The graph stays connected when the blockages are omitted from it. The SDT begins from a certain vertex and aims to identify a route without any blocked edges which detects the target with minimum total traveling and search cost. We analyze this problem from a competitive analysis perspective under two scenarios with and without blockages. For the scenario with blockages, we provide a tight lower bound on the competitive ratio of deterministic solutions, an optimal deterministic solution, a randomized solution with a bounded expected competitive ratio, together with lower and upper bounds on the expected competitive ratio of the optimal randomized solutions. For the scenario without blockages, we provide tight lower bounds as well as optimal deterministic and randomized solutions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Competitive analysis; Online blocked edges; Routing; Searching |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Management School (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 23 Aug 2022 13:41 |
Last Modified: | 23 Aug 2022 13:41 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s10878-022-00876-9 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:190031 |