WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
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Two related problems are considered. The first is determining whether it is possible to triangulate a vertex-colored graph without introducing edges between vertices of the same color. This is related to a fundamental problem for geneticists, that of using character state information to construct evolutionary trees. The polynomial equivalence of these problems is demonstrated. An important subproblem arises when the characters are based on DNA sequences. Such characters assume up to four states. An O(n/sup 2/k) algorithm, where n is the number of species and k is the number of characters, is presented for this case.