Graph Searching and Related Problems

Bonato, Anthony; Yang, Boting

doi:10.1007/978-1-4419-7997-1_76

Cited by 35 publications

(16 citation statements)

References 130 publications

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“…Kehagias and Pralat [16] analyzed the expected capture time of a drunk robber whose strategy is 82:3 simply a random walk on the graph. For a broader overview of the results on the game of Cops and Robbers, the reader is referred to the book of Bonato and Nowakowski [9] and recent surveys [3,10,12,15].…”

Section: Related Literaturementioning

confidence: 99%

A tight lower bound for the capture time of the Cops and Robbers game

Brandt

Emek

Uitto

et al. 2020

Theoretical Computer Science

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For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k ≥ 2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(n k+1), however, no non-trivial lower bounds were previously known; indeed, in their 2011 book, Bonato and Nowakowski ask whether this upper bound can be improved. In this paper, the question of Bonato and Nowakowski is answered on the negative, proving that the O(n k+1) bound is asymptotically tight for any constant k ≥ 2. This yields a surprising gap in the capture time complexities between the 1-cop and the 2-cop cases.

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Section: Related Literaturementioning

confidence: 99%

A tight lower bound for the capture time of the Cops and Robbers game

Brandt

Emek

Uitto

et al. 2020

Theoretical Computer Science

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“…Graph search problems have been studied extensively but not in exactly this form. The literature on this is vast and we refer to Bonato and Yang (2013) for an extensive review.…”

Section: Cdpmentioning

confidence: 99%

The Chinese deliveryman problem

Sitters

2019

4OR-Q J Oper Res

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We introduce the Chinese deliveryman problem where the goal of the deliveryman is to visit every house in his neighborhood such that the average time of arrival is minimized. We show that, in contrast to the well-known Chinese postman problem, the Chinese deliveryman problem is APX-hard in general and NP-hard for planar graphs. We give a simple √ 2-approximation for undirected graphs and a 4/3-approximation for 2-edge connected graphs. We observe that there is a PTAS for planar graphs and that depth first search is optimal for trees. Keywords Chinese deliveryman problem • Approximation algorithms • Computational complexity • Chinese postman problem • Graph search Mathematics Subject Classification 90C27 • 68Q17 • 90C59 1 Citation from Grötschel and Yuan (2012).

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“…A graph searching game is a game where searchers (or cops) want to capture a fugitive (or robber) and the fugitive want to escape from the searchers, and they move through a graph for their purpose. Graph searching games have been well-studied [1] [2] [3], since graph searching games have many practical and theoretical applications such as robot motion planning, network security, and artificial intelligence (see e.g. [4]).…”

Section: Introductionmentioning

confidence: 99%

Equivalence between Linear Tangle and Maximal Single Ideal

Fujita¹,

Yamazaki²

2019

OJDM

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The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and single ideal. This short report gives an alternative proof of the equivalence.

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Graph Searching and Related Problems

Cited by 35 publications

References 130 publications

A tight lower bound for the capture time of the Cops and Robbers game

A tight lower bound for the capture time of the Cops and Robbers game

The Chinese deliveryman problem

Equivalence between Linear Tangle and Maximal Single Ideal

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