Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
On search decision and the efficiency of polynomial-time algorithms
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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 vertex separation and search number of a graph
Information and Computation
Eavesdropping games: a graph-theoretic approach to privacy in distributed systems
Journal of the ACM (JACM)
Edge and node searching problems on trees
Theoretical Computer Science - computing and combinatorics
Computing the vertex separation of unicyclic graphs
Information and Computation
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Searching Trees with Sources and Targets
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Edge Search Number of Cographs in Linear Time
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Edge search number of cographs
Discrete Applied Mathematics
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In this paper, we study the problem of computing the minimum number of searchers who can capture an intruder hiding in a graph. We propose a linear time algorithm for computing the vertex separation and the optimal layout for a unicyclic graph. The best algorithm known so far is given by Ellis et al. (2004) and needs O(n log n) time, where n is the number of vertices in the graph. By a linear-time transformation, we can compute the search number and the optimal search strategy for a unicyclic graph in linear time. We show how to compute the search number for a k-ary cycle-disjoint graph. We also present some results on approximation algorithms.