Algorithms and Complexity: 7th International Conference, by Ricardo Baeza-Yates (auth.), Tiziana Calamoneri, Josep Diaz

By Ricardo Baeza-Yates (auth.), Tiziana Calamoneri, Josep Diaz (eds.)

This e-book constitutes the refereed complaints of the seventh foreign convention on Algorithms and Computation, CIAC 2010, held in Rome, Italy, in may possibly 2010. The 30 revised complete papers offered including three invited papers have been rigorously reviewed and chosen from 114 submissions. one of the themes addressed are graph algorithms I, computational complexity, graph coloring, tree algorithms and tree decompositions, computational geometry, video game conception, graph algorithms II, and string algorithms.

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Extra info for Algorithms and Complexity: 7th International Conference, CIAC 2010, Rome, Italy, May 26-28, 2010. Proceedings

Sample text

While favorable branching rules exist, the algorithm proceeds by applying the branch and reduce paradigm. 3645n) upper bound will never be exceeded. – When the algorithm reaches a search state where favorable branching rules are no longer possible, an instance of the Weighted Steiner Tree problem is generated to solve the remaining part of the problem. This either-or approach can be applied, potentially, to other problems whenever the absence of favorable branching conditions leads to a reduction of the input instance to some manageable size.

Thus V (T ) ∩ B is a red-blue dominating set of G. – Every red vertex is a leaf node in T . Otherwise, some red vertex u would have (at least) two blue neighbors, v and w, in T . Removing one if the two edges, say uv, and connecting v to w via a path of blue vertices (since B is connected), gives a steiner tree of smaller weight (since the weight of any path connecting blue vertices is bounded above by n − 1). Since every red vertex is a leaf node, V (T ) ∩ B is connected. And since every edge that connects internal nodes of T is of weight 1, the number of internal nodes in T is minimum.

Consider the problems VERTEX COVER and INDEPENDENT SET where we have to decide whether a graph contains a vertex cover1 of 1 A vertex cover is a subset of the nodes satisfying that every edge has at least one endpoint in the set. Maximizing PageRank with New Backlinks 39 size k or an independent set2 of size k respectively. FPT is contained in the complexity class W[1] = {P : P ≤ INDEPENDENT SET}. Even though VERTEX COVER is NP-complete it has been solved for large n and k = 400 [11]. The reason is that VERTEX COVER ∈ FPT with moderate f and c.

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