A strongly polynomial minimum cost circulation algorithm
Combinatorica
Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On minimizing width in linear layouts
Discrete Applied Mathematics
Monotonicity in graph searching
Journal of Algorithms
The vertex separation number of a graph equals its path-width
Information Processing Letters
Recontamination does not help to search a graph
Journal of the ACM (JACM)
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
On the pathwidth of chordal graphs
Discrete Applied Mathematics - ARIDAM IV and V
The vertex separation and search number of a graph
Information and Computation
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
Algorithms and obstructions for linear-width and related search parameters
Discrete Applied Mathematics
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
Computing Optimal Linear Layouts of Trees in Linear Time
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Coordinated exploration of unknown labyrinthine environments applied to the pursuit evasion problem
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
Lower bounds on the pathwidth of some grid-like graphs
Discrete Applied Mathematics
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
The impact of adversarial knowledge on adversarial planning in perimeter patrol
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 1
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems: industrial track
Visibility-based pursuit-evasion with limited field of view
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Algorithms and complexity results for pursuit-evasion problems
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Pursuit-evasion on trees by robot teams
IEEE Transactions on Robotics
Improving the Efficiency of Clearing with Multi-agent Teams
International Journal of Robotics Research
Search in the physical world
A graph search algorithm for indoor pursuit/evasion
Mathematical and Computer Modelling: An International Journal
A pursuit-evasion problem-solving strategy based on probability estimation in a planer region
International Journal of Computing Science and Mathematics
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We study the classical edge-searching pursuit-evasion problem where a number of pursuers have to clear a given graph of fast-moving evaders despite poor visibility, for example, where robots search a cave system to ensure that no terrorists are hiding in it. We study when polynomial-time algorithms exist to determine how many robots are needed to clear a given graph (minimum robot problem) and how a given number of robots should move on the graph to clear it with either a minimum sum of their travel distances (minimum distance problem) or minimum task-completion time (minimum time problem). The robots cannot clear a graph if the vertex connectivity of some part of the graph exceeds the number of robots. Researchers therefore focus on graphs whose subgraphs can always be cut at a limited number of vertices, that is, graphs of low treewidth, typically trees. We describe an optimal polynomial-time algorithm, called CLEARTHETREE, that is shorter and algorithmically simpler than the state-of-the-art algorithm for the minimum robot problem on unit-width unit-length trees. We then generalize prior research to both unit-width arbitrary-length and unit-length arbitrary-width graphs and derive both algorithms and time complexity results for a variety of graph topologies. Pursuit-evasion problems on the former graphs are generally simpler than pursuit-evasion problems on the latter graphs. For example, the minimum robot and distance problems are solvable in polynomial time on unit-width arbitrary-length trees but NP-hard on unit-length arbitrary-width trees.