tailieunhanh - Báo cáo toán học: "Reversal Distance for Strings with Duplicates: Linear Time Approximation using Hitting Set"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Reversal Distance for Strings with Duplicates: Linear Time Approximation using Hitting Set. | Reversal Distance for Strings with Duplicates Linear Time Approximation using Hitting Set Petr Kolman Charles University in Prague Faculty of Mathematics and Physics Department of Applied Mathematics kolman@ Tomasz WaleT Warsaw University Faculty of Mathematics Informatics and Mechanics walen@ Submitted Nov 14 2006 Accepted Mar 30 2007 Published Jul 19 2007 Mathematics Subject Classification 68W25 68R15 92D20 Abstract In the last decade there has been an ongoing interest in string comparison problems to a large extend the interest was stimulated by genome rearrangement problems in computational biology but related problems appear in many other areas of computer science. Particular attention has been given to the problem of sorting by reversals SBR given two strings A and B find the minimum number of reversals that transform the string A into the string B a reversal p i j i j transforms a string A ai .an into a string A0 ai . ai-iaj aj-i. a-iOj i. an . Closely related is the minimum common string partition problem MCSP given two strings A and B find a minimum size partition of A into substrings Pi . Pl . A Pi .Pl and a partition of B into substrings Qi . Qi such that Qi . Qi is a permutation of Pi . Pi . Primarily the SBR problem has been studied for strings in which every symbol appears exactly once that is for permutations and only recently attention has been given to the general case where duplicates of the symbols are allowed. In this paper we consider the problem k-SBR a version of SBR in which each symbol is allowed to appear up to k times in each string for some k 1. The main result of the paper is a k -approximation algorithm for k-SBR running in time O n compared to the previously known algorithm for k-SBR this is an improvement by Supported by project 1M0021620808 ITI of Ministry of Education of the Czech Republic. y Supported by the Polish Scientific Research Committee KBN under grant GR-1946. THE ELECTRONIC JOURNAL OF .