Solving parametric problems on trees
Journal of Algorithms
Dynamic trees and dynamic point location
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Optimal parametric search on graphs of bounded tree-width
Journal of Algorithms
Bounds for parametric sequence comparison
Discrete Applied Mathematics
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Efficient sensitivity analysis algorithms are presented for two problems arising in the study of Markov models of sequence evolution: ancestral reconstruction in evolutionary trees and local ungapped alignment under log-odds scoring. The algorithms generate complete descriptions of the optimum solutions for all possible values of the evolutionary distance. The running time for the parametric ancestral reconstruction problem under the Kimura 2-parameter model is O(kn + kn2/3 log k), where n is the number of sequences and k is their length, assuming all edges have the same length. For the parametric gapless alignment problem under the Jukes-Cantor model, the running time is O(mn + mn2/3 log m), where m and n are the sequence lengths and n ≤ m.