269 research outputs found
On the computational complexity of a game of cops and robbers
We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme (1984) [1]. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at the same speed. The players are allowed to pick their starting positions at the first move. The question of the computational complexity of deciding this game was raised by Goldstein and Reingold (1995) [9]. We prove that the game is hard for PSPACE.Ă©2012 Elsevier B.V. All rights reserved
Visibility Graphs, Dismantlability, and the Cops and Robbers Game
We study versions of cop and robber pursuit-evasion games on the visibility
graphs of polygons, and inside polygons with straight and curved sides. Each
player has full information about the other player's location, players take
turns, and the robber is captured when the cop arrives at the same point as the
robber. In visibility graphs we show the cop can always win because visibility
graphs are dismantlable, which is interesting as one of the few results
relating visibility graphs to other known graph classes. We extend this to show
that the cop wins games in which players move along straight line segments
inside any polygon and, more generally, inside any simply connected planar
region with a reasonable boundary. Essentially, our problem is a type of
pursuit-evasion using the link metric rather than the Euclidean metric, and our
result provides an interesting class of infinite cop-win graphs.Comment: 23 page
Cops and Robbers is EXPTIME-complete
We investigate the computational complexity of deciding whether k cops can
capture a robber on a graph G. In 1995, Goldstein and Reingold conjectured that
the problem is EXPTIME-complete when both G and k are part of the input; we
prove this conjecture.Comment: v2: updated figures and slightly clarified some minor point
Characterizations and algorithms for generalized Cops and Robbers games
We propose a definition of generalized Cops and Robbers games where there are
two players, the Pursuer and the Evader, who each move via prescribed rules. If
the Pursuer can ensure that the game enters into a fixed set of final
positions, then the Pursuer wins; otherwise, the Evader wins. A relational
characterization of the games where the Pursuer wins is provided. A precise
formula is given for the length of the game, along with an algorithm for
computing if the Pursuer has a winning strategy whose complexity is a function
of the parameters of the game. For games where the position of one player does
not affect the available moves of he other, a vertex elimination ordering
characterization, analogous to a cop-win ordering, is given for when the
Pursuer has a winning strategy
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-HĂŒbner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro PezzĂ©, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Localization game on geometric and planar graphs
The main topic of this paper is motivated by a localization problem in
cellular networks. Given a graph we want to localize a walking agent by
checking his distance to as few vertices as possible. The model we introduce is
based on a pursuit graph game that resembles the famous Cops and Robbers game.
It can be considered as a game theoretic variant of the \emph{metric dimension}
of a graph. We provide upper bounds on the related graph invariant ,
defined as the least number of cops needed to localize the robber on a graph
, for several classes of graphs (trees, bipartite graphs, etc). Our main
result is that, surprisingly, there exists planar graphs of treewidth and
unbounded . On a positive side, we prove that is bounded
by the pathwidth of . We then show that the algorithmic problem of
determining is NP-hard in graphs with diameter at most .
Finally, we show that at most one cop can approximate (arbitrary close) the
location of the robber in the Euclidean plane
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