Download PDF by Allan Borodin (auth.), Frank Dehne, Alejandro López-Ortiz,: Algorithms and Data Structures: 9th International Workshop,

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By Allan Borodin (auth.), Frank Dehne, Alejandro López-Ortiz, Jörg-Rüdiger Sack (eds.)

ISBN-10: 3540281010

ISBN-13: 9783540281016

ISBN-10: 3540317112

ISBN-13: 9783540317111

This publication constitutes the refereed complaints of the ninth overseas Workshop on Algorithms and information constructions, WADS 2005, held in Waterloo, Canada, in August 2005.

The 37 revised complete papers provided have been rigorously reviewed and chosen from ninety submissions. A large number of themes in algorithmics and knowledge constructions is addressed together with looking out and sorting, approximation, graph and community computations, computational geometry, randomization, communications, combinatorial optimization, scheduling, routing, navigation, coding, and development matching.

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Extra resources for Algorithms and Data Structures: 9th International Workshop, WADS 2005, Waterloo, Canada, August 15-17, 2005. Proceedings

Sample text

Altogether, we thus end up with a problem kernel of 22k ·2k 2 = O(4k ·k 2 ) vertices. It remains to justify the polynomial running time. First, note that the trivial factor-2 approximation algorithm runs in time O(|E|) = O(n2 ). Second, examining the common neighborhoods can be done in O(n2 ) time by successively partitioning the vertices in V \ S according to their neighborhoods. Clearly, a simple brute-force search within the reduced instance (with a size of only O(4k · k 2 ) vertices) already yields the fixed-parameter tractability of k 2 CVC, albeit in time proportional to 4 k·k .

2. There exists v ∈ V for which tv > tv . It follows that our algorithm obtains a feasible primal solution within v∈V kv steps, since if this number of steps was already performed, we have tv = kv for every v ∈ V , and all edges are covered by the associated primal solution. Implementing a Single Step. We assume that when a step begins we are given a feasible dual solution (y, z) such that T (v) = ∅ for every v ∈ V , and an edge (p, q) that is not covered by the associated primal solution, that is, rtpp + rtqq < lp,q .

11 Cor. 12 problem is known to have a factor-2 approximation [10]. Answering an open question from [5], we show that this problem appears to be fixed-parameter intractable—it is W[1]-hard. The same is proven for its minimization version. Summarizing, we emphasize that our main focus is on deciding between fixedparameter tractability and W[1]-hardness for all of the considered problems. Interestingly, although all considered problems behave in more or less the same way from the viewpoint of polynomial-time approximability—all have factor-2 approximations—the picture becomes completely different from a parameterized complexity point of view: Maximum Partial Vertex Cover appears to be intractable and Capacitated Vertex Cover appears to be significantly harder than Connected Vertex Cover.

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Algorithms and Data Structures: 9th International Workshop, WADS 2005, Waterloo, Canada, August 15-17, 2005. Proceedings by Allan Borodin (auth.), Frank Dehne, Alejandro López-Ortiz, Jörg-Rüdiger Sack (eds.)


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