TY - JOUR

T1 - Weighted LCS

AU - Amir, Amihood

AU - Gotthilf, Zvi

AU - Shalom, B. Riva

PY - 2010/9

Y1 - 2010/9

N2 - The Longest Common Subsequence (LCS) of two strings A,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 LCS problem of z sequences in time O(znz+1). For the second, we consider the log-probability version of the problem, prove NP-hardness and provide an approximation algorithm.

AB - The Longest Common Subsequence (LCS) of two strings A,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 LCS problem of z sequences in time O(znz+1). For the second, we consider the log-probability version of the problem, prove NP-hardness and provide an approximation algorithm.

KW - Approximation algorithms

KW - NP-hard problem

KW - Position weight matrix

KW - String algorithms

UR - http://www.scopus.com/inward/record.url?scp=77955688622&partnerID=8YFLogxK

U2 - 10.1016/j.jda.2010.02.001

DO - 10.1016/j.jda.2010.02.001

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AN - SCOPUS:77955688622

SN - 1570-8667

VL - 8

SP - 273

EP - 281

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

IS - 3

ER -