By Kazuo Iwama (auth.), Tetsuo Asano (eds.)
This booklet constitutes the refereed lawsuits of the seventeenth overseas Symposium on Algorithms and Computation, ISAAC 2006, held in Kolkata, India in December 2006.
The seventy three revised complete papers offered have been conscientiously reviewed and chosen from 255 submissions. The papers are equipped in topical sections on algorithms and information constructions, on-line algorithms, approximation set of rules, graphs, computational geometry, computational complexity, community, optimization and biology, combinatorial optimization and quantum computing, in addition to allotted computing and cryptography.
Read or Download Algorithms and Computation: 17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006. Proceedings PDF
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Additional info for Algorithms and Computation: 17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006. Proceedings
By combining the pathwidth bounds of Lemma 3 and the running time of the algorithm of Lemma 2, we obtain that MMM can be solved Branching and Treewidth Based Exact Algorithms 21 in time O(max(3(1·5«) 6 3¬ )n ) when the path decomposition part of the algorithm is executed. Assume now that the path decomposition part is not executed. Then, the algorithm continues to branch when the maximum degree ¡(H) of the graph H is 3. And so, C «n when ¡(H) first becomes 3. At this point, the set C has been obtained by branching on vertices of degree at least 4 and we investigate the number of subproblems obtained so far.
Graham Higman. Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society. Third Series, 2:326–336, 1952. 32. David S. Johnson. The NP-completeness column: an ongoing guide (column 19). Journal of Algorithms, 8(3):438–448, 1987. 33. Iyad Kanj and Ljubomir Perkovi´c. Improved parameterized algorithms for planar dominating set. In Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science (MFCS 2002), volume 2420 of Lecture Notes in Computer Science, pages 399–410, 2002.
Then the algorithm stops without backtracking. A minimum maximal matching can then be found using the pathwidth algorithm of Lemma 2. Enumerate minimal vertex covers. The algorithm enumerates all minimal vertex covers of H. For every minimal vertex cover Q of H, S C Q is a vertex cover of G and the characterization of Proposition 2 is used to find a minimum maximal matching of G. The conditions under which these di«erent parts are executed have been carefully chosen to optimize the overall running time of the algorithm, including the pathwidth algorithm of Lemma 2.