Theoretical Computer Science
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The complexity of searching a graph
Journal of the ACM (JACM)
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
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
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
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Helicopter search problems, bandwidth and pathwidth
Discrete Applied Mathematics
Eavesdropping games: a graph-theoretic approach to privacy in distributed systems
Journal of the ACM (JACM)
Graph Searching and Interval Completion
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Searching expenditure and interval graphs
Discrete Applied Mathematics
Finite graph automata for linear and boundary graph languages
Theoretical Computer Science
Parameterized Complexity
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Graph searching is the game of capturing a fugitive by a team of searchers in a network. There are equivalent characterizations in terms of path-width, interval thickness, and vertex separation. So far the interest has mainly focused on the search number of a graph, which is the minimal the number of searchers to win the game, and accordingly on the width and the thickness. These parameters measure the needed resources and correspond to space complexity. As its dual, we introduce the search time, which has not yet been studied in graph searching. We prove that all main results on graph searching can be generalized to include search time, such as monotone or recontamination free graph searching, and the characterizations in terms of path-width, interval graphs, and vertex separation, for which we introduce appropriate length parameters. We establish the NP-completeness of both search-width and search-time. Finally we investigate the speed-up by an extra searcher. There are ’good’ classes of graphs where a single extra searcher reduces the search time to one half and ’bad’ ones where some extra searchers are no real help.