Search-hide games on trees

Search-hide games on trees In this paper we consider search-hide games on trees. There are two players. Player H (the hider or inspectee) selects one of m vertices of the tree for hiding ‘undeclared objects’ permanently. Player I (the inspector) is allowed to search some vertices of the tree trying to find the hidden objects. However, player I can only examine exactly k (< m ) vertices lying on a subtree with k vertices because of certain limitations. Player I wants to maximize the probability of detecting the undeclared objects and player H to minimize it. This problem can be described by a fractional covering problem (FC) and its dual (DFC). An algorithm based on the revised simplex method with implicit column generation is proposed for solving FC and DFC. The all possible strategies of the player I (all possible subtree with k vertices) is not necessary listed explicitly. In order to find a profitable column, a polynomial algorithm is developed by utilizing the structure of the underlying tree. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png European Journal of Operational Research Elsevier

Search-hide games on trees

European Journal of Operational Research, Volume 80 (1) – Jan 5, 1995

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Publisher
Elsevier
Copyright
Copyright © 1995 Elsevier Ltd
ISSN
0377-2217
eISSN
1872-6860
DOI
10.1016/0377-2217(93)E0362-2
Publisher site
See Article on Publisher Site

Abstract

In this paper we consider search-hide games on trees. There are two players. Player H (the hider or inspectee) selects one of m vertices of the tree for hiding ‘undeclared objects’ permanently. Player I (the inspector) is allowed to search some vertices of the tree trying to find the hidden objects. However, player I can only examine exactly k (< m ) vertices lying on a subtree with k vertices because of certain limitations. Player I wants to maximize the probability of detecting the undeclared objects and player H to minimize it. This problem can be described by a fractional covering problem (FC) and its dual (DFC). An algorithm based on the revised simplex method with implicit column generation is proposed for solving FC and DFC. The all possible strategies of the player I (all possible subtree with k vertices) is not necessary listed explicitly. In order to find a profitable column, a polynomial algorithm is developed by utilizing the structure of the underlying tree.

Journal

European Journal of Operational ResearchElsevier

Published: Jan 5, 1995

References

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