Limited visibility Cops and Robber

Clarke, Nancy E.; Cox, Danielle; Duffy, Christopher; Dyer, Danny; Fitzpatrick, Shannon L.; Messinger, Margaret-Ellen

doi:10.1016/j.dam.2019.12.007

Cited by 13 publications

(15 citation statements)

References 20 publications

(34 reference statements)

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“…The visibility of the cops is limited to the distance between the cops and the robber within k range, so this model is called the k-visibility cops and robber game. In this case, related results can be found in [7,8].…”

Section: Introductionsupporting

confidence: 57%

Lower Bound of Zero-visibility Cops and Robber Game on the Cube Grid

Wang¹,

Zhong²

2020

Computer Science &Amp; Information Technology (CS &Amp; IT)

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Zero-visibility cops and robber game is a variant of the classical model. The robber is invisible in the zero-visibility game. In this paper, we study the zero-visibility cops and robber game on the cube grid. We first study a partition problem of the cube grid. Then we prove the lower bound on the zero-visibility cop number of the cube grid by using the results in the partition. We also show the lower bound is a quadratic polynomial about n.

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Section: Introductionsupporting

confidence: 57%

Lower Bound of Zero-visibility Cops and Robber Game on the Cube Grid

Wang¹,

Zhong²

2020

Computer Science &Amp; Information Technology (CS &Amp; IT)

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“…The first formulation appears in [34]. Further progress was achieved in the Master's theses [21,33] and, recently, in [11,12,13] (for the zero-visibility case) and in [8] (for the general case, which includes zero-and completevisibility as special cases). A somewhat different approach to the invisible robber appears in [23,24] and a related computational approach is presented in [22].…”

Section: Introductionmentioning

confidence: 99%

“…Lines 6-20: using Dijkstra's algorithm, we find a shortest path between the all-dirty vertex and every all-clear vertex of G I . 8 4. Lines 21-22: the algorithm returns the overall shortest path.…”

mentioning

confidence: 99%

An Algorithm for Limited Visibility Graph Searching

Kehagias¹,

Papazoglou²

2021

Preprint

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We study a graph search problem in which a team of searchers attempts to find a mobile target located in a graph. Assuming that (a) the visibility field of the searchers is limited, (b) the searchers have unit speed and (c) the target has infinite speed, we formulate the Limited Visibility Graph Search (LVGS) problem and present the LVGS algorithm, which produces a search schedule guaranteed to find the target in the minimum possible number of steps. Our LVGS algorithm is a "conversion" of Guibas and Lavalle's polygonal region search algorithm .

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“…Several pursuit and evasion games have been studied with imperfect information and this is a common theme in graph searching; see [7,9] for surveys. A recent variant [8] of Cops and Robbers fixes a visibility threshold for the cops, where the cops can only see vertices within their kth neighborhood, for a fixed non-negative integer k.…”

Section: Introductionmentioning

confidence: 99%

“…While a priori it might appear that there should be a relationship between the hyperopic cop number and the 1-visibility cop number c v,1 from [8] (as hyperopic cops only see the robber on the complements of their neighbor sets), there is no elementary relationship between the parameters. In particular, there are graphs G such that c H (G) = c v,1 (G), where G is the complement of G. To see this, note that c H (K n ) = n 2 (which we will prove in Theorem 3), while c v,1 (K n ) = n. Hence, there exist families of graphs G such that |c H (G) − c v,1 (G)| is arbitrarily large.…”

Section: Introductionmentioning

confidence: 99%

Hyperopic Cops and Robbers

Bonato¹,

Clarke²,

Cox³

et al. 2019

Theoretical Computer Science

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We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in [0, 1/2].

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Limited visibility Cops and Robber

Cited by 13 publications

References 20 publications

Lower Bound of Zero-visibility Cops and Robber Game on the Cube Grid

Lower Bound of Zero-visibility Cops and Robber Game on the Cube Grid

An Algorithm for Limited Visibility Graph Searching

Hyperopic Cops and Robbers

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