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 ebook constitutes the refereed court cases of the seventh overseas convention on Algorithms and Computation, CIAC 2010, held in Rome, Italy, in may possibly 2010. The 30 revised complete papers provided including three invited papers have been rigorously reviewed and chosen from 114 submissions. one of the issues addressed are graph algorithms I, computational complexity, graph coloring, tree algorithms and tree decompositions, computational geometry, online game thought, graph algorithms II, and string algorithms.

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

Example text

5. Accordingly, we distinguish two possible cases: (i) When |B| < αn, then the crbds problem is solvable by exhaustive enumeration of all subsets of B in O∗ (2αn ). (ii) When |B| ≥ αn, then the crbds problem is solvable via the wst algorithm in O∗ (2(1−α)n ). 4143n). In the following section, we show how to obtain a better worst-case run-time. 4 An Improved Exact Algorithm We shall assume the given instance has the following three subsets of vertices: (i) the set D of blue vertices that must belong to an optimum solution, (ii) the set B of remaining blue vertices, and (iii) the set R of red vertices that are yet to be dominated.

Liedloff Additional work is needed to determine whether the reduction to wst can be replaced by direct work on the crbds instance, and to make use of the fact that the terminal nodes (or red vertices) form an independent set in the wst instance. Moreover, we note that the use of measure and conquer in the branching phase might not lead to a better run-time since there may be worst-case instances for which favorable branching conditions do not hold. References 1. : Connected dominating set in sensor networks and manets.

The order in which the branching occurs is important for attaining the desired runtime. e. in decreasing order) and branches accordingly. After every branch, the previously considered vertices can be discarded which further reduces the size of the instance. Additional favorable branching rules are derived when considering degree two vertices in R∪D. Whenever we exclude one of the neighbors of such a vertex the other must automatically be added to an optimum solution to ensure that An Exact Algorithm for Connected Red-Blue Dominating Set 31 the vertex is dominated.

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