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Computing and Combinatorics: 17th Annual International by Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto (auth.), Bin

By Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto (auth.), Bin Fu, Ding-Zhu Du (eds.)

This publication constitutes the refereed complaints of the sixteenth Annual overseas convention on Computing and Combinatorics, held in Dallas, TX, united states, in August 2011. The fifty four revised complete papers offered have been rigorously reviewed and chosen from 136 submissions. issues coated are algorithms and knowledge buildings; algorithmic video game thought and on-line algorithms; automata, languages, common sense, and computability; combinatorics concerning algorithms and complexity; complexity thought; computational studying thought and data discovery; cryptography, reliability and safety, and database idea; computational biology and bioinformatics; computational algebra, geometry, and quantity thought; graph drawing and knowledge visualization; graph concept, verbal exchange networks, and optimization; parallel and disbursed computing.

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Extra resources for Computing and Combinatorics: 17th Annual International Conference, COCOON 2011, Dallas, TX, USA, August 14-16, 2011. Proceedings

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Let i be a leaf of T , and u0 , . . , ud be the sequence of nodes of T from the root r to i satisfying that u0 = r, ud = i and u is a child of u −1 for each ∈ {1, . . , d}. Further, let v be the child of u −1 different from u . The flush operation F LUSH(i) turns cj and wj into c˜j and w ˜j in the following way. – c˜j (u ) = 1 for all ∈ {0, . . , d − 1}. Dominating Set Counting in Graph Classes – w ˜ j (u ) = wj (u ) · cj (u) and w ˜j (v ) = wj (v ) · u∈Anc(u ) ∈ {1, . . , d}. ˜ j (u) = wj (u) for all other u.

11] show how to select a subsequence whose density is closest to a given density δ in O(n log2 n) time. Without the upper bound on the length B an optimal O(n log n)-time algorithm is given. The Density Maximization Problem in Graphs 27 Subsequently, this problem has been generalized to graphs. Hsieh et al. [8,7] show that a maximum density path in a tree subject to lower and upper length bounds can be computed in time O(Bn) and that it is NP-hard to find a maximum density subtree in a tree, for which they also presented an O(B 2 n) time algorithm.

Proof. Without loss of generality we may assume that T is a binary tree. Otherwise we can make it binary by adding dummy edges with weight and length 0 in linear time. A centroid of a binary tree is a vertex whose removal disconnects T into at most 3 subtrees with at most half of the vertices of the original tree in each of the subtrees. We root T in one of its centroids r. Let v1 , v2 be two children of r and let R be the path between v1 and v2 via r. Then we can compute the maximum density path including R using tangent queries in time O(n log2 n) as follows: First, we compute the set P1 of paths starting in v1 .

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