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Bounding an Optimal Search Path with a Game of Cop and Robber on Graphs
"... Abstract. In search theory, the goal of the Optimal Search Path (OSP) problem is to find a finite length path maximizing the probability that a searcher detects a lost wanderer on a graph. We propose to bound the probability of finding the wanderer in the remaining search time by relaxing the proble ..."
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Abstract. In search theory, the goal of the Optimal Search Path (OSP) problem is to find a finite length path maximizing the probability that a searcher detects a lost wanderer on a graph. We propose to bound the probability of finding the wanderer in the remaining search time by relaxing
A GAME OF COPS AND ROBBERS
, 1984
"... Let G be a finite connected graph. Two players, called cop C and robber R, play a game on G according to the following rules. First C then R occupy some vertex of G. After that they move alternately along edges of G. The cop C wins if he succeeds in putting himself on top of the robber R, otherwise ..."
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Cited by 124 (0 self)
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Let G be a finite connected graph. Two players, called cop C and robber R, play a game on G according to the following rules. First C then R occupy some vertex of G. After that they move alternately along edges of G. The cop C wins if he succeeds in putting himself on top of the robber R, otherwise
Bounds for Cops and Robber Pursuit
, 2009
"... Abstract. We prove that the robber can evade (that is, stay at least unit distance from) at least ⌊n/5.889 ⌋ cops patroling an n × n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always captu ..."
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Abstract. We prove that the robber can evade (that is, stay at least unit distance from) at least ⌊n/5.889 ⌋ cops patroling an n × n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always
Addendum: Relaxation of the Optimal Search Path Problem with the Cop and Robber Game
"... Abstract. In the Optimal Search Path problem from search theory, the objective is to find a finite length searcher’s path that maximizes the probability of detecting a lost wanderer on a graph. We introduce a novel bound on the probability of finding the wanderer in the remaining search time and dis ..."
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Abstract. In the Optimal Search Path problem from search theory, the objective is to find a finite length searcher’s path that maximizes the probability of detecting a lost wanderer on a graph. We introduce a novel bound on the probability of finding the wanderer in the remaining search time
Cops and robber game with a fast robber
, 2011
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Graph searching problems are described as games played ..."
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Cited by 1 (1 self)
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that the cop number (the minimum number of cops that can always capture the robber) of a connected graph on n vertices is O( n). We consider a version of the Cops and Robber game, where the robber is faster than the cops, but is not allowed to jump over the cops. This version was first studied in 2008. We show
The Role of Information in the CopRobber Game
, 2008
"... We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber’s vertex. In the standard formulation, it is assumed tha ..."
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Cited by 8 (1 self)
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We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber’s vertex. In the standard formulation, it is assumed
CONJECTURES ON COPS AND ROBBERS
"... Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop number of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1. ..."
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Abstract. We consider some of the most important conjectures in the study of the game of Cops and Robbers and the cop number of a graph. The conjectures touch on diverse areas such as algorithmic, topological, and structural graph theory. 1.
THE COPS AND ROBBER GAME ON GRAPHS WITH FORBIDDEN (INDUCED) SUBGRAPHS
, 2008
"... The twoplayer, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cop ..."
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Cited by 5 (0 self)
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The twoplayer, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number
Variations on Cops and Robbers
"... We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R> 1 edges at a time, establishing a general upper bound of n/α (1−o(1))√logα n 1, where α = 1 + R, thus generalizing the best known upper bound for the classical case R = 1 due to ..."
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Cited by 10 (1 self)
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We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R> 1 edges at a time, establishing a general upper bound of n/α (1−o(1))√logα n 1, where α = 1 + R, thus generalizing the best known upper bound for the classical case R = 1 due
Results 1  10
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1,160