By Manuel Blum (auth.), My T. Thai, Sartaj Sahni (eds.)
This publication constitutes the court cases of the sixteenth Annual foreign convention on Computing and Combinatorics, held in Nha Trang, Vietnam, in July 2010.
Read Online or Download Computing and Combinatorics: 16th Annual International Conference, COCOON 2010, Nha Trang, Vietnam, July 19-21, 2010. Proceedings PDF
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Extra info for Computing and Combinatorics: 16th Annual International Conference, COCOON 2010, Nha Trang, Vietnam, July 19-21, 2010. Proceedings
The Art of Computer Programming, 3rd edn. Seminumerical Algorithms, vol. 3. Addison-Wesley, Reading (1998) 22. : Enumerate and Expand: Improved algorithms for Connected Vertex Cover and Tree Cover. Theory of Computing Systems 43(2), 234–253 (2008) 23. : Splitters and near-optimal derandomization. In: 36th Annual Symposium on Foundations of Computer Science (FOCS ’95), pp. 182–193. IEEE Computer Society Press, Los Alamitos (1995) 24. : An algorithm for a minimum cover of a graph. Proceedings of the American Mathematical Society 10, 315–319 (1959) 25.
Suppose there exists a PPT from P to Q. Then, if Q has a polynomial kernel, then P also has a polynomial kernel. The Curse of Connectivity: t-Total Vertex (Edge) Cover 37 Theorem 1. For each fixed t ≥ 2, t-tvc has no kernel of size bounded by k c , for any fixed constant c, unless PH collapses to the third level 1 . Proof. We begin by noting that by a simple reduction from the NP-complete Set Cover problem , the derived classical problem corresponding to RBDS is NP-complete. Also, the derived classical problem corresponding to t-tvc is evidently in NP.
Using this instead of a random coloring, we obtain the desired deterministic algorithm. 1k+O(log k) . 3 Total Edge Covers For each positive integer t, the parameterized t-total edge cover problem was deﬁned in the Introduction. For t = 1, t-tec is the k-ec problem, which is solvable in polynomial time  while for t ≥ 2, the problem is NP-complete [12, Theorem 3]. We use the following fact to obtain an equivalent formulation of the problem. 40 H. Fernau et al. Fact 4. (From the proof of [12, Theorem 16]) In any connected graph G with n vertices, and for any t < n, there exists a minimal t-TEC, say S, of G such that the graph G(S) induced by the edge set S is acyclic.