Theoretical Computer Science
Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
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
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
Approximating the pathwidth of outerplanar graphs
Information Processing Letters
Approximation of pathwidth of outerplanar graphs
Journal of Algorithms
A 3-approximation for the pathwidth of Halin graphs
Journal of Discrete Algorithms
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Edge Search Number of Cographs in Linear Time
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Pathwidth is NP-Hard for Weighted Trees
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Pathwidth of circular-arc graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Searching cycle-disjoint graphs
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Edge search number of cographs
Discrete Applied Mathematics
Approximate search strategies for weighted trees
Theoretical Computer Science
Hi-index | 0.00 |
We describe an O(n log n) algorithm for the computation of the vertex separation of unicyclic graphs. The algorithm also computes a linear layout with optimal vertex separation in the same time bound. Pathwidth, node search number and vertex separation are different ways of defining the same notion. Path decompositions and search strategies can be derived from linear layouts. The algorithm applies existing, linear time, techniques for the computation of the vertex separation of trees together with corresponding optimal layouts. We reformulate the earlier work on the linear time computation of optimal layouts. A polynomial time algorithm for the problem on unicyclic graphs can be inferred from existing more general methods for graphs of fixed treewidth, since unicyclic graphs have treewidth two, but the time complexity of the resulting method would seem to be an inordinately high order polynomial. Our algorithm we claim is "practical." The addition of one edge to a tree does seem to require a considerably more elaborate algorithm.