Abstract
The Longest Common Subsequence (LCS) of two strings A and B is a well studied problem having a wide range of applications. When each symbol of the input strings is assigned a positive weight the problem becomes the Heaviest Common Subsequence (HCS) problem. In this paper we consider a different version of weighted LCS on Position Weight Matrices (PWM). The Position Weight Matrix was introduced as a tool to handle a set of sequences that are not identical, yet, have many local similarities. Such a weighted sequence is a ‘statistical image' of this set where we are given the probability of every symbol's occurrence at every text location. We consider two possible definitions of LCS on PWM. For the first, we solve the weighted LCS problem of z sequences in time O(zn z + 1). For the second, we prove NPNP-hardness and provide an approximation algorithm.
| Original language | American English |
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| Title of host publication | 20th International Workshop on Combinatorial Algorithms (IWOCA 2009) |
| Editors | Jiří Fiala, Jan Kratochvíl, Mirka Miller |
| Publisher | Springer Berlin Heidelberg |
| State | Published - 2009 |