Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object

Abstract

This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. AbstractA Searcher seeks to …nd a stationary Hider located at some point H (not necessarily a node) on a given network Q. The Searcher can move along the network from a given starting point at unit speed, but to actually …nd the Hider she must pass it while moving at a …xed slower speed (which may depend on the arc). In this 'bimodal search game', the payo¤ is the …rst time the Searcher passes the Hider while moving at her slow speed. This game models the search for a small or well hidden object (e.g., a contact lens, improvised explosive device, predator search for camou ‡aged prey). We de…ne a Bimodal Chinese Postman tour as a tour of minimum time which traverses every point of every arc at least once in the slow mode. For trees and weakly Eulerian networks (networks containing a number of disjoint Eulerian cycles connected in a tree-like fashion) the value of the bimodal search game is =2. For trees, the optimal Hider strategy has full support on the network. This di¤ers from traditional search games, where it is optimal for him to hide only at leaf nodes. We then consider the notion of a lucky Searcher who can also detect the Hider with a positive probability q even when passing him at her fast speed. This paper has particular importance for demining problems.

Optimal search and ambush for a hider who can escape the search region

“…If we interpret s 0 (t) as the speed of the searcher, the assumption that at high speed he is less likely to spot a ‡eeing hider is in accordance with empirical data and other search models (e.g. Alpern and Lidbetter (2015)). In our model, the searcher is noisy, and his speed s 0 (t) (the probability or intensity of searching) is detectable by the hider.…”

Search for an immobile hider on a stochastic network

“…Lidbetter (2013, 2019a) replaced the usual pathwise search with what they call expanding search, where the searched area of a rooted network expands over different paths from the origin at different speeds chosen by the searcher, in such a way that the sum of the speeds is fixed. Alpern and Lidbetter (2015) dealt with a situation where the searcher can choose one of two speeds to travel and can detect the hider, when passing in front of him, only if she travels at the lower speed. Alpern (2017) considered a model where the hider can hide anywhere in a network and the searcher has to entirely traverse an edge before being able to turn around.…”

Approximate solutions for expanding search games on general networks

“…Search games on lattices were studied by Zoroa et al (2013). The possibility that the Searcher might have to choose between two or more speeds of search was considered by Alpern and Lidbetter (2015). The case where simply reaching the hidden object is not enough to find it is considered by Baston and Kikuta (2015), who posit a cost for searching, in addition to traveling.…”