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Searching and sweeping graphs: A brief survey
 Matematiche
, 2006
"... This papers surveys some of the work done on trying to capture an intruder in a graph. If the intruder may be located only at vertices, the term searching is employed. If the intruder may be located at vertices or along edges, the term sweeping is employed. There are a wide variety of applications f ..."
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Cited by 42 (2 self)
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This papers surveys some of the work done on trying to capture an intruder in a graph. If the intruder may be located only at vertices, the term searching is employed. If the intruder may be located at vertices or along edges, the term sweeping is employed. There are a wide variety of applications for searching and sweeping. Old results, new results and active research directions are discussed. 1
Randomized PursuitEvasion with Local Visibility
 SIAM Journal on Discrete Mathematics
, 2006
"... We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce ..."
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Cited by 41 (2 self)
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We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunterwin, that is, if a single hunter can capture a rabbit of either kind on G.
A better bound for the cop number of general graphs
 Journal of Graph Theory
, 2008
"... Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to ..."
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Cited by 22 (2 self)
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Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to
Search and pursuitevasion in mobile robotics
 Autonomous Robots
"... (will be inserted by the editor) ..."
Capturing an evader in a polygonal environment with obstacles
 22nd International Joint Conference on Artificial Intelligence
"... We study a pursuitevasion game in which one or more cops try to capture a robber by moving onto the robber’s current location. All players have equal maximum velocities. They can observe each other at all times. We show that three cops can capture the robber in any polygonal environment (which can ..."
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Cited by 20 (8 self)
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We study a pursuitevasion game in which one or more cops try to capture a robber by moving onto the robber’s current location. All players have equal maximum velocities. They can observe each other at all times. We show that three cops can capture the robber in any polygonal environment (which can contain any finite number of holes). 1
Randomized pursuitevasion with limited visibility
, 2003
"... We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffi ..."
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Cited by 20 (2 self)
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We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunterwin, that is, if a single hunter can capture a rabbit of either kind on G.
Reasoning About Strategies: On the ModelChecking Problem
, 2011
"... In open systems veri cation, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ..."
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Cited by 18 (15 self)
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In open systems veri cation, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multiagent games, such as Atl, Atl ∗ , and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHPSl, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHPSl is obtained by using rstorder quanti cations over strategies and has been investigated in the very speci c setting of twoagents turnedbased games, where a nonelementary modelchecking algorithm has been provided. While CHPSl is a very expressive logic, we claim that it does not fully capture the strategic aspects of multiagent systems. In this paper, we introduce and study a more general strategy logic, denoted Sl, for reasoning about strategies in multiagent concurrent games. We prove that Sl includes CHPSl, while maintaining a decidable modelchecking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHPSl. Moreover, we prove that such a problem for Sl is NonElementarySpacehard. This negative result has spurred us to investigate here syntactic fragments of Sl, strictly subsuming Atl ∗ , with the hope of obtaining an elementary modelchecking problem. Among the others, we study the
COPS AND ROBBERS IN A RANDOM GRAPH
, 2008
"... We consider the pursuit and evasion game on finite, connected, undirected graphs known as cops and robbers. Meyniel conjectured that for every graph on n vertices O(n 1 2) cops can win the game. We prove that this holds up to a log(n) factor for random graphs G(n, p) if p is not very small, and this ..."
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Cited by 18 (0 self)
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We consider the pursuit and evasion game on finite, connected, undirected graphs known as cops and robbers. Meyniel conjectured that for every graph on n vertices O(n 1 2) cops can win the game. We prove that this holds up to a log(n) factor for random graphs G(n, p) if p is not very small, and this is close to be tight unless the graph is very dense. We analyze the are a defending strategy (used by Aigner in case of planar graphs) and show examples where it can not be too efficient.
On Meyniel’s conjecture of the cop number
, 2009
"... Meyniel conjectured the cop number c(G) of any connected graph G on n vertices is at most C √ n for some constant C. In this paper, we prove Meyniel’s conjecture in special cases that G has diameter at most 2 or G is a bipartite graph with diameter at most 3. For general connected graphs, n we prove ..."
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Cited by 17 (0 self)
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Meyniel conjectured the cop number c(G) of any connected graph G on n vertices is at most C √ n for some constant C. In this paper, we prove Meyniel’s conjecture in special cases that G has diameter at most 2 or G is a bipartite graph with diameter at most 3. For general connected graphs, n we prove c(G) = O (), improving the best previously known upperbound O ( n ln n 1