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

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

This ebook constitutes the refereed court cases 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. subject matters lined are algorithms and knowledge buildings; algorithmic online game thought and on-line algorithms; automata, languages, good judgment, and computability; combinatorics relating to algorithms and complexity; complexity idea; computational studying thought and information discovery; cryptography, reliability and safety, and database idea; computational biology and bioinformatics; computational algebra, geometry, and quantity idea; graph drawing and data visualization; graph conception, conversation networks, and optimization; parallel and allotted computing.

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Read Online or Download Computing and Combinatorics: 17th Annual International Conference, COCOON 2011, Dallas, TX, USA, August 14-16, 2011. Proceedings PDF

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

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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. Wu et al. [19,18] improve on this by presenting an optimal algorithm for computing a maximum density path in a tree in time O(n log n) in the presence of both a lower and upper length bounds. They also give an O(n log2 n) algorithm for finding a heaviest path in a tree in the presence of length constraints [19], which is improved to O(n log n) by Liu and Chao [13] .

In the analysis of our algorithms, the time complexity refers to the number of arithmetic operations, not bit operations. Due to the space constraint, we postpone the proofs of theorems/lemmas with * marks to the full version. 2 Interval Graphs A graph G = ({1, . . , n}, E) is interval if there exists a set {I1 , . . , In } of closed intervals on a real line such that {i, j} ∈ E if and only if Ii ∩ Ij = ∅. Such a set of intervals is called an interval representation of G. It is known that there always exists an interval representation in which the endpoints of intervals are all distinct, and we can find such a representation of a given interval graph that is sorted by their right endpoints in O(n + m) time [1], where n is the number of vertices and m is the number of edges.

J (u) = wj (u) for all other u. – c˜j (u) = cj (u) and w 19 cj (u) for all u∈Anc(v ) Note that the operation can be performed in O(log n) time in a top-down manner, since d = O(log n). Also observe that c˜j and w ˜ j satisfy conditions (1) and (2), and hence j s(i, j) = w ˜ (i). We now discuss how to perform each step in more detail. In Step 1, we need to identify i∗∗ (j) and i∗ (j). To find i∗∗ (j), we look for the rightmost interval {I1 , . . ) Here, the rightmost interval means the interval with rightmost right endpoint.

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