By Jack Edmonds (auth.), Jiří Fiala, Jan Kratochvíl, Mirka Miller (eds.)

This publication constitutes the revised chosen papers of the 20 th overseas Workshop on Combinatorial Algorithms, held in June/July 2009 within the fort of Hradec nad Moravicí, Czech Republic.

The forty-one papers integrated during this quantity including five invited papers have been conscientiously reviewed and chosen from over a hundred submissions. the themes handled are algorithms and knowledge constructions, functions, combinatorial enumeration, combinatorial optimization, complexity conception, computational biology, databases, decompositions and combinatorial designs, discrete and computational geometry, together with graph drawing, and graph conception and combinatorics.

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Example text

Obviously best1,1 , yields the proper value. k Consider now li,j . i], implying there exists another common subsequence of length k with probability x such that x < x . h]. In the former case, the x subsequence can include a match k of B[i], a matching of A[j] or neither of them. Since li,j maximizes the values k k of li−1,j , li,j−1 , the assumption implies that there exists another subsequence of k k length k with probability x where max{li−1,j , li,j−1 } < x contradicting the ink k duction hypothesis of optimal value of li ,j , i < i, or j < j.

The case of Amir et. al. [3] is the special case in our model where all probabilities of the sequences equal one. 3 Longest Common Weighted Subsequence (LCWS) The resemblance between the HCS and LCWS problems lies in the weight demands on the common subsequence. However, there is a substantial difference between the problems. The HCS maximizes a single parameter – the weight – whereas the LCWS maximizes the length under a weight restriction. The weight bound does force the algorithm to maximize the weight at every step, yet not as a goal but rather as a byproduct.

E. when Δ is fixed a priori. The algorithm is not polynomial, since it has been shown in [10] that some instances can be represented in O(log n) space and the problem restricted to these instances remains N P -hard. Hence, when Δ is fixed, the proposed algorithm requires a time which is polynomial in n, that is pseudo-polynomial in the size of the instances. For practical contexts, Δ << n is a reasonable restriction, since we may require that in at most Δ steps (independently from the input instance) a possible delay must be absorbed.

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