Nondeterministic Graph Searching: From Pathwidth to Treewidth
- 107 Downloads
We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this game-theoretic approach and graph decompositions called q -branched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of q-branched tree decompositions. The equivalence between nondeterministic graph searching and q-branched tree decomposition enables us to design an exact (exponential time) algorithm computing q-branched treewidth for all q≥0, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers.
KeywordsTreewidth Pathwidth Graph searching
Unable to display preview. Download preview PDF.
- 1.Amini, O., Huc, F., Perennes, S.: On the pathwidth of planar Graphs. SIAM J. Discret. Math. (to appear) Google Scholar
- 2.Amir, E.: Efficient approximation for triangulation of minimum treewidth, In: Uncertainty in Artificial Intelligence: Proceedings of the Seventeenth Conference (UAI-2001), San Francisco, CA, pp. 7–15. Morgan Kaufmann (2001) Google Scholar
- 8.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999) Google Scholar
- 12.Fomin, F.V., Kratsch, D., Todinca, I.: Exact algorithms for treewidth and minimum fill-in. In: Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP 2004). Lecture Notes in Computer Science, vol. 3142, pp. 568–580. Springer, Berlin (2004) Google Scholar
- 13.Goldsmith, J., Levy, M., Munhenk, M.: Limited Nondeterminism. SIGACT News, Introduction to Complexity Theory, Column 13, June 1996 Google Scholar
- 18.Mazoit, F., Nisse, N.: Monotonicity property of non-deterministic graph searching. In: Proceedings of the 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2007) (to appear) Google Scholar