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Open AccessArticle

A Distributed Approach to the Evasion Problem

1
Computer Science, CUNY Graduate Center, 365 5th Ave, New York, NY 10016, USA
2
Mathematics, CUNY College of Staten Island, 2800 Victory Blvd, Staten Island, NY 10314, USA
3
Mathematics and Computer Science, CUNY John Jay College, 524 W 59th St, New York, NY 10019, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Algorithms 2020, 13(6), 149; https://doi.org/10.3390/a13060149
Received: 28 April 2020 / Revised: 14 June 2020 / Accepted: 19 June 2020 / Published: 23 June 2020
(This article belongs to the Special Issue Topological Data Analysis)
The Evasion Problem is the question of whether—given a collection of sensors and a particular movement pattern over time—it is possible to stay undetected within the domain over the same stretch of time. It has been studied using topological techniques since 2006—with sufficient conditions for non-existence of an Evasion Path provided by de Silva and Ghrist; sufficient and necessary conditions with extended sensor capabilities provided by Adams and Carlsson; and sufficient and necessary conditions using sheaf theory by Krishnan and Ghrist. In this paper, we propose three algorithms for the Evasion Problem: one distributed algorithm extension of Adams’ approach for evasion path detection, and two different approaches to evasion path enumeration. View Full-Text
Keywords: evasion path; distributed algorithm evasion path; distributed algorithm
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Khryashchev, D.; Chu, J.; Vejdemo-Johansson, M.; Ji, P. A Distributed Approach to the Evasion Problem. Algorithms 2020, 13, 149.

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