| Title: | Guarding a subgraph as a tool in pursuit-evasion games |
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| Authors: | ID Bokal, Drago (Author)
ID Jerebic, Janja (Author) |
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| Files: |  https://sciendo.com/article/10.7151/dmgt.2244
 Guarding_a_Subgraph_as_a_Tool_in_Pu-Bokal-2022.pdf (377,93 KB)
MD5: 11963C3EA41A404EDFA1E31318385747
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
FOV - Faculty of Organizational Sciences in Kranj
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| Abstract: | Pursuit-evasion games study the number of cops needed to capture therobber in a game played on a graph, in which the cops and the robber movealternatively to neighbouring vertices, and the robber is captured if a copsteps on the vertex the robber is in. A common tool in analyzing this copnumber of a graph is a cop moving along a shortest path in a graph, thuspreventing the robber to step onto this path. We generalize this approach byintroducing a shadow of the robber, the maximal set of vertices from whichthe cop parries the protected subgraph. In this context, the robber becomesan intruder and the cop becomes the guard. We show that the shadow canbe computed in polynomial time, implying polynomial time algorithms forcomputing both a successful guard as well as a successful intruder, whicheverexists. Furthermore, we show that shadow function generalizes the conceptof graph retractions. In some cases, this implies a polynomially computablecertification of the negative answer to the NP-complete problem of existenceof a retraction to a given subgraph. |
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| Keywords: | pursuit-evasion game, graph searching, guarding, shadow function, graph retraction |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2022 |
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| Year of publishing: | 2021 |
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| Number of pages: | str. 123-138 |
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| Numbering: | Vol. 42, no. 1 |
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| PID: | 20.500.12556/DKUM-85071  |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| COBISS.SI-ID: | 8147219 |
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| Publication date in DKUM: | 17.08.2023 |
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| Views: | 555 |
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| Downloads: | 68 |
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| Metadata: |    |
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| Categories: | Misc.
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