Search for an immobile entity on a network

Jotshi, Arun; Batta, Rajan

doi:10.1016/j.ejor.2007.08.032

Cited by 23 publications

(17 citation statements)

References 16 publications

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“…Under such searches, the portion S (t) of the search region that has been covered by time t expands in a continuous way until the …rst time T (the search time) that it contains the target of the search. This is the …rst article to give a rigorous de…nition and analysis of expanding search on a network that is comparable to the well known theory developed for pathwise search by Gal (1979Gal ( , 2000Gal ( , 2011, Baston and Bostock (1990), Anderson and Aramendia (1990), Kikuta and Ruckle (1994), Pavlovic (1995), Reynierse and Potter (1993), Alpern and Gal (2003), Jotshi and Batta (2008), Alpern (2010Alpern ( , 2011. The work of Alpern and Howard (2000) considered a related problem of a single Searcher who alternates between looking for a single Hider at two locations, which can now be seen as a special case (on a star network) of expanding search.…”

Section: Introductionmentioning

confidence: 99%

Mining Coal or Finding Terrorists: The Expanding Search Paradigm

Alpern

Lidbetter

2013

Operations Research

107

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We show how to optimize the search for a hidden object, terrorist, or simply Hider, located at a point H according to a known or unknown distribution on a rooted network Q. We modify the traditional 'pathwise search' approach to a more general notion of 'expanding search'. When the Hider is restricted to the nodes of Q; an expanding search S consists of an ordering (a 1 ; a 2 ; : : : ) of the arcs of a spanning subtree such that the root node is in a 1 and every arc a i is adjacent to a previous arc a j ; j < i: If a k contains H; the search time T is (a 1 ) + + (a k ) ; where is length measure on Q: For more general distributions ; an expanding search S is described by the nested family of connected sets S (t) which specify the area of Q that has been covered by time t: S (0) is the root, (S (t)) = t; and T = min ft : H 2 S (t)g : For a known Hider distribution on a tree Q; the expected time minimizing strategy S begins with the rooted subtree Q 0 maximizing the 'density' (Q 0 ) = (Q 0 ) : (For arbitrary networks, we use this criterion on all spanning subtrees.) The search S can be interpreted as the optimal method of mining known coal seams, when the time to move miners or machines is negligible compared to digging time. When the Hider distribution is unknown, we consider the zero-sum search game where the Hider picks H; the Searcher S and the payo¤ is T: For trees Q; the value is V = ( (Q) + D) =2, where D is a mean distance from root to leaf nodes. If Q is 2 arc connected, V = (Q) =2. Applications and interpretations of the expanding search paradigm are given, particularly to multiple agent search.

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Section: Introductionmentioning

confidence: 99%

Mining Coal or Finding Terrorists: The Expanding Search Paradigm

Alpern

Lidbetter

2013

Operations Research

107

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“…Hide‐and‐seek problems consider an intruder that “hides” in a stationary location, while the searchers try to locate the intruder in minimum time . Such problems also arise in search‐and‐rescue settings .…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…The CPP seeks a route that visits each edge exactly once, and starts and ends from the same node (see the classical work of Edmonds and Johnson ). Relevant to our study, Jotshi and Batta examine strategies that minimize the expected time required to find a stationary hider on a network given a single searcher. In contrast to their study, we focus on exact rather than heuristic methods, and consider both the presence of multiple searchers and the case of mobile intruders.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Branch‐cut‐price algorithms for solving a class of search problems on general graphs

Taşkın

Smith

2017

Networks

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We consider graph search problems involving an intruder and mobile searchers. The graph consists of nodes on which the intruder and searchers may be located, and edges on which these entities travel. Associated with each node is a set of nodes that are visible from that node. The goal is to find the minimum number of searchers needed to detect the intruder within a given time limit. We investigate three variants of the graph search problem: (i) a hide‐and‐seek problem, in which a stationary intruder “hides” at an unknown node, (ii) a pursuit‐evasion problem, in which the intruder moves among the nodes to avoid being detected, and (iii) a patrol problem, which is similar to the pursuit‐evasion problem except that searchers patrol the graph in repeated circuits to seek intruders. Our contribution provides exponential‐size set‐covering formulations for these problems, along with a class of branch‐cut‐price algorithms tailored for solving them. These algorithms leverage results from the orienteering literature to solve pricing problems related to searcher routes. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 4–18 2017

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“…For general networks there are methods of approximating the solution (Anderson and Aramedia [8]) and analyses of the complexity of the solution (von Stengel and Werchner [22]). More applied work in this area has been carried out by Jotshi and Batta [16]. The topic of search games has been the subject of books by Gal [12], Alpern and Gal [6], and Garnaev [14].…”

Section: T (S; H)d(s H)mentioning

confidence: 99%

Searching a Variable Speed Network

Alpern¹,

Lidbetter

2014

Mathematics of OR

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A point H lies on a network Q according to some unknown distribution. A Searcher starts at a given point O of Q and moves to …nd H at speeds which depend on his location and direction. He seeks the randomized search algorithm which minimizes the expected search time. This is equivalent to modeling the problem as a zero-sum hide-and-seek game whose value V is called the search value of (Q; O).We make a new and direct derivation of an explicit formula V = (1=2) ( + ) for the search value of a tree, where is the minimum tour time of Q and (called the incline of Q) is an average over the leaf nodes i of the di¤er-; where d (x; y) is the time to go from x to y: The function can be interpreted as height, assuming uphill is slower than downhill. We then apply this formula to obtain numerous results for general networks. We also introduce a new general method of comparing the search value of networks which di¤er in a single arc. Some simple networks have very complicated optimal strategies which require mixing of a continuum of pure strategies. Many of our results generalize analogous ones obtained for constant velocity (in both directions) by S. Gal, but not all of those results can be extended.

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Search for an immobile entity on a network

Cited by 23 publications

References 16 publications

Mining Coal or Finding Terrorists: The Expanding Search Paradigm

Mining Coal or Finding Terrorists: The Expanding Search Paradigm

Branch‐cut‐price algorithms for solving a class of search problems on general graphs

Searching a Variable Speed Network

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