49 research outputs found
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
The Cop Number of the One-Cop-Moves Game on Planar Graphs
Cops and robbers is a vertex-pursuit game played on graphs. In the classical
cops-and-robbers game, a set of cops and a robber occupy the vertices of the
graph and move alternately along the graph's edges with perfect information
about each other's positions. If a cop eventually occupies the same vertex as
the robber, then the cops win; the robber wins if she can indefinitely evade
capture. Aigner and Frommer established that in every connected planar graph,
three cops are sufficient to capture a single robber. In this paper, we
consider a recently studied variant of the cops-and-robbers game, alternately
called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers
game, where at most one cop can move during any round. We show that Aigner and
Frommer's result does not generalise to this game variant by constructing a
connected planar graph on which a robber can indefinitely evade three cops in
the one-cop-moves game. This answers a question recently raised by Sullivan,
Townsend and Werzanski.Comment: 32 page
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, 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