Cop vs. Gambler

Komarov, Natasha; Winkler, Peter

doi:10.1016/j.disc.2016.01.015

Cited by 2 publications

(16 citation statements)

References 11 publications

(16 reference statements)

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“…Komarov and Winkler introduced the gambler in [14]. The cop and gambler play on a connected n-vertex graph.…”

Section: Introductionmentioning

confidence: 99%

“…The gambler was motivated by a problem in software design [14]. Suppose that an anti-incursion program must navigate a linked list of ports in order to minimize the interception time for an enemy packet.…”

Section: Introductionmentioning

confidence: 99%

“…The known gambler models the case when the enemy's port distribution is known, while the unknown gambler models the case when the port distribution is unknown. Komarov and Winkler proved that if both the cop and known gambler use best play, then the known gambler has expected capture time n for any connected n-vertex graph [14]. They also found a pursuit algorithm for all connected n-vertex graphs that has expected capture time at most approximately 1.97n for the unknown gambler.…”

Section: Introductionmentioning

confidence: 99%

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Expected capture time and throttling number for cop versus gambler

Geneson,

Quines,

Slettnes

et al. 2019

Preprint

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We bound expected capture time and throttling number for the cop versus gambler game on a connected graph with n vertices, a variant of the cop versus robber game that is played in darkness, where the adversary hops between vertices using a fixed probability distribution. The paper that originally defined the cop versus gambler game focused on two versions, a known gambler whose distribution the cop knows, and an unknown gambler whose distribution is secret. We define a new version of the gambler where the cop makes a fixed number of observations before the lights go out and the game begins. We show that the strategy that gives the best possible expected capture time of n for the known gambler can also be used to achieve nearly the same expected capture time against the observed gambler when the cop makes a sufficiently large number of observations. We also show that even with only a single observation, the cop is able to achieve an expected capture time of approximately 1.5n, which is much lower than the expected capture time of the best known strategy against the unknown gambler (approximately 1.95n).

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“…Komarov and Winkler introduced the gambler in [14]. The cop and gambler play on a connected n-vertex graph.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Expected capture time and throttling number for cop versus gambler

Geneson,

Quines,

Slettnes

et al. 2019

Preprint

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“…Models which focus on finding an invisible target rather than catching a visible one have been the focus of much recent work. In the Hunter versus Rabbit game, studied by Adler, Räcke, Sivadasan, Sohler and Vöcking [1] and the Cop versus Gambler game, studied by Komarov and Winkler, [16] the aim is to catch a randomly-moving target as quickly as possible; in both cases the searcher is restricted to moving on the edges of the underlying graph, but the target is not. Related models can be used to design protocols for ad-hoc mobile networks [5].…”

Section: Introductionmentioning

confidence: 99%

“…In Cop versus Gambler, the gambler's strategy is simply a probability distribution on the vertices, and his location at different time steps is independent. In this setting Komarov and Winkler showed that a cop who knows this probability distribution can achieve expected capture time n, which is trivially best possible for the uniform distribution, and a cop who does not know the distribution can still achieve capture time O(n) [16].…”

Section: Introductionmentioning

confidence: 99%

Locating a robber with multiple probes

Haslegrave

Johnson

Koch

2018

Discrete Mathematics

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We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager (Seager, 2012). Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph G there is a winning strategy for the cop on the graph G 1/m obtained by replacing each edge of G by a path of length m, if m ≥ n (Carragher et al., 2012). The present authors showed that, for all but a few small values of n, this bound may be improved to m ≥ n/2, which is best possible (Haslegrave et al., 2016b). In this paper we consider the natural extension in which the cop probes a set of k vertices, rather than a single vertex, at each turn. We consider the relationship between the value of k required to ensure victory on the original graph with the length of subdivisions required to ensure victory with k = 1. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of k for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree ∆, which is best possible up to a factor of (1 − o(1)).

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Cop vs. Gambler

Cited by 2 publications

References 11 publications

Expected capture time and throttling number for cop versus gambler

Expected capture time and throttling number for cop versus gambler

Locating a robber with multiple probes

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