The complexity of zero-visibility cops and robber

Dereniowski, Dariusz; Dyer, Danny; Tifenbach, Ryan M.; Yang, Boting

doi:10.1016/j.tcs.2015.03.022

Cited by 22 publications

(17 citation statements)

References 7 publications

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“…We use T k h to denote a perfect k-ary tree with height h. Notice that the 1-visibility cop number of a perfect k-ary tree can be computed by Algorithm 1. Similarly, from Theorem 3.6 in [7], we can show that c 0 (T…”

Section: Perfect K-ary Treesmentioning

confidence: 60%

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One-visibility cops and robber on trees

Yang

Akter

2021

Theoretical Computer Science

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Section: Perfect K-ary Treesmentioning

confidence: 60%

“…Tang [16] gave a quadratic time algorithm for computing the zero-visibility cop number of trees. Dereniowski et al [7] improved this result by presenting a linear-time algorithm. They also proved that the problem of determining the zero-visibility cop number of a graph is NP-complete.…”

Section: Cops and Robber Gamementioning

confidence: 98%

One-visibility cops and robber on trees

Yang

Akter

2021

Theoretical Computer Science

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“…Further results on this variant can be found in the work by Frieze et al [26]. Yet another interesting variant of the Cops and Robber game where the robber is invisible has been also studied in the literature (see [20], and the references therein).…”

Section: Related Literature On "Cops and Robbers" Gamesmentioning

confidence: 97%

Greedy strategies and larger islands of tractability for conjunctive queries and constraint satisfaction problems

Greco

Scarcello

2017

Information and Computation

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Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in artificial intelligence, or more generally of the homomorphism problem over relational structures. These methods work on the hypergraph structure of problem instances. Each method provides a way of transforming any cyclic hypergraph into an acyclic one, by organizing its edges (or its nodes) into a polynomial number of clusters, and by suitably arranging these clusters as a tree, called decomposition tree. Then, by using such a tree (or by just knowing that any exists) the given problem instance can be solved in polynomial time.Most structural decomposition methods can be characterized through hypergraph games that are variations of the Robber and Cops graph game that characterizes the notion of treewidth. In particular, decomposition trees somehow correspond to monotone winning strategies, where the escape space of the robber on the hypergraph is shrunk monotonically by the cops. In fact, unlike the treewidth case, there are hypergraphs where monotonic strategies do not exist, while the robber can be captured by means of more complex non-monotonic strategies. However, these powerful strategies do not correspond in general to valid decompositions.The paper provides a general way to exploit the power of non-monotonic strategies, by allowing a "disciplined" form of non-monotonicity, characteristic of cops playing in a greedy way. It is shown that deciding the existence of a (non-monotone) greedy winning strategy (and compute one, if any) is tractable. Moreover, despite their nonmonotonicity, such strategies always induce valid decomposition trees, which can be computed efficiently based on them. As a consequence, greedy strategies allow us to define new islands of tractability for the considered problems, properly including all previously known classes of tractable instances. In particular, we define the new notion of greedy hypertree decomposition of a hypergraph, whose associated notion of width is at most the hypertree width, and sometimes strictly smaller.

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“…Tošić [9] studied the zero-visibility cop numbers of paths, cycles, complete graphs, and complete bipartite graphs. Tang [11] proposed a quadratic time algorithm to determine the zero-visibility cop number of a tree, then a linear algorithm of a tree was given by Dereniowskl [12]. In the above articles, only simple graphs were studied, and there is no better method to determine the zero-visibility cop number until Dereniowskl [13] studied the relationship between the monotonic zero-visibility cop number and the path width of a graph.…”

Section: Related Workmentioning

confidence: 99%

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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The complexity of zero-visibility cops and robber

Cited by 22 publications

References 7 publications

One-visibility cops and robber on trees

One-visibility cops and robber on trees

Greedy strategies and larger islands of tractability for conjunctive queries and constraint satisfaction problems

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

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