| Records |
| Author |
Fomin, F.V.; Golovach, P.A.; Kratochvil, J.; Nisse, N.; Suchan, K. |
| Title |
Pursuing a fast robber on a graph |
Type |
|
| Year |
2010 |
Publication |
Theoretical Computer Science |
Abbreviated Journal |
Theor. Comput. Sci. |
| Volume |
411 |
Issue |
7-9 |
Pages |
1167-1181 |
| Keywords |
Pursuit-evasion game on graphs; Cops and Robbers; Complexity; Parameterized complexity; Cliquewidth; Planar graph |
| Abstract |
The Cops and Robbers game as originally defined independently by Quilliot and by Nowakowski and Winkler in the 1980s has been Much Studied, but very few results pertain to the algorithmic and complexity aspects of it. In this paper we prove that computing the minimum number of cops that are guaranteed to catch a robber on a given graph is NP-hard and that the parameterized version of the problem is W[2]-hard; the proof extends to the case where the robber moves s time faster than the cops. We show that on split graphs, the problem is polynomially solvable if s = 1 but is NP-hard if s = 2. We further prove that on graphs of bounded cliquewidth the problem is polynomially solvable for s <= 2. Finally, we show that for planar graphs the minimum number of cops is unbounded if the robber is faster than the cops. (C) 2009 Elsevier B.V. All rights reserved. |
| Address |
[Fomin, Fedor V.; Golovach, Petr A.] Univ Bergen, Dept Informat, N-5020 Bergen, Norway, Email: petr.golovach@durham.ac.uk |
| Corporate Author |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0304-3975 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000274886700020 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
83 |
| Permanent link to this record |
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| Author |
Golovach, P.A.; Heggernes, P.; Lima, P.T.; Montealegre, P. |
| Title |
Finding connected secluded subgraphs |
Type |
|
| Year |
2020 |
Publication |
Journal Of Computer And System Sciences |
Abbreviated Journal |
J. Comput. Syst. Sci. |
| Volume |
113 |
Issue |
|
Pages |
101-124 |
| Keywords |
Secluded subgraph; Parameterized complexity; Forbidden subgraphs |
| Abstract |
Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. However, for many applications, it is desirable that the found subgraph has as few connections to the rest of the graph as possible, which gives rise to the SECLUDED Pi-SUBGRAPH problem. Here, input k is the size of the desired subgraph, and input t is a limit on the number of neighbors this subgraph has in the rest of the graph. This problem has been studied from a parameterized perspective, and unfortunately it turns out to be W[1]-hard for many graph properties Pi, even when parameterized by k + t. We show that the situation changes when we are looking for a connected induced subgraph satisfying Pi. In particular, we show that the CONNECTED SECLUDED Pi-SUBGRAPH problem is FPT when parameterized by just t for many important graph properties Pi. (C) 2020 Elsevier Inc. All rights reserved. |
| Address |
[Golovach, Petr A.; Heggernes, Pinar; Lima, Paloma T.] Univ Bergen, Dept Informat, N-5020 Bergen, Norway, Email: petr.golovach@uib.no; |
| Corporate Author |
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Thesis |
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| Publisher |
Academic Press Inc Elsevier Science |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0022-0000 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000539435200006 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1191 |
| Permanent link to this record |
