The complexity of searching a graph
Journal of the ACM (JACM)
Monotonicity in graph searching
Journal of Algorithms
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
The vertex separation and search number of a graph
Information and Computation
SIAM Journal on Control and Optimization
Minimax Rendezvous on the Line
SIAM Journal on Control and Optimization
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
On the Complexity of Decontaminating an Hexagonal Mesh Network
ICCGI '07 Proceedings of the International Multi-Conference on Computing in the Global Information Technology
Distributed chasing of network intruders
Theoretical Computer Science
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Decontamination of hypercubes by mobile agents
Networks - Games, Interdiction, and Human Interaction Problems on Networks
Network search games, with arbitrary searcher starting point
Networks - Games, Interdiction, and Human Interaction Problems on Networks
Tree Decontamination with Temporary Immunity
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Cleaning an arbitrary regular network with mobile agents
ICDCIT'05 Proceedings of the Second international conference on Distributed Computing and Internet Technology
Intrusion detection with mobile agents
Computer Communications
Cutting plane algorithms for solving a stochastic edge-partition problem
Discrete Optimization
The integer L-shaped method for stochastic integer programs with complete recourse
Operations Research Letters
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This article considers the problem of using synchronous mobile agents to decontaminate the nodes of a graph given a spreading contamination. We begin by considering the problem of minimizing cleaning time, given initial agent, and contamination locations. Then, we take as input a set of all possible locations in which a contamination can start and examine problems in which we strategically preposition agents. In one problem, we minimize the number of agents and prescribe their initial locations, so that the graph can be cleaned within a time limit for any potential initial contamination. We also determine the best initial locations for some predetermined number of agents to minimize expected cleaning time, given probability estimates of potential initial contamination locations. We analyze the complexity of each variant and formulate the problems as mixed-integer programs. As an alternative method, we also provide a construction heuristic for the cleaning problem and cutting-plane algorithms for the agent location problems. Computational results using these approaches demonstrate the efficacy of our procedures. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013 © 2013 Wiley Periodicals, Inc.