Combinatorial Algorithms: 20th International Workshop, IWOCA by Jack Edmonds (auth.), Jiří Fiala, Jan Kratochvíl, Mirka

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

This e-book constitutes the revised chosen papers of the twentieth 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 subjects handled are algorithms and information constructions, functions, combinatorial enumeration, combinatorial optimization, complexity concept, computational biology, databases, decompositions and combinatorial designs, discrete and computational geometry, together with graph drawing, and graph idea and combinatorics.

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However, the price of robustness is kept low as in the previous instances. 5 Conclusion We have presented algorithm SAΔ for solving the problem of planning robust timetables when the input event activity network topology is a tree. The algorithm ensures that, if a delay occurs, no more than Δ activities are influenced by Evaluation of Recoverable-Robust Timetables on Tree Networks 35 the propagation of such a delay. We have shown the performances of SAΔ both theoretically and experimentally. Despite the problem is proved to be N P -hard, the obtained results show the applicability of the algorithm to ensure robust timetables with respect to bounded delays.

The LCS problem had also been investigated on more general structures such as trees and matrices [2], run-length encoded strings [4], and more. Another structure, useful in molecular biology, is the weighted sequence. |S|. While comparing two weighted sequences we define a weight function, W , assigning a value to every possible match between two characters one from the first sequence and the other from the second sequence. The LCS variant for these weighted sequences aims at maximizing the weight of the common subsequence, instead of its length as hereafter defined: Definition 2.

Given a subtree Tv , No (Tv ) denotes the set of nodes y such that (x, y) ∈ A, x ∈ Tv and y ∈ Tv . We denote by w(Tv ) the value x∈Tv w(x) and by |Tv | the number of nodes contained in Tv . Note that, in order to compute all the values w(Tv ) for each v ∈ V , one visit of Tr is sufficient. In the next lemma, we prove that for any instance, there exists a RTT -optimal solution which assigns only slack times of size α. Lemma 1. Given an instance i of RTT , for each solution Π for i, there exists a solution Π for i such that f (Π ) ≤ f (Π) and, for each arc a = (x, y), either Π (y) = Π (x) + L(a) or Π (y) = Π (x) + L(a) + α.

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