A three-string approach to the closest string problem

Authors:
Zhi-Zhong Chen;Bin Ma;Lusheng Wang
Affiliations:
Department of Mathematical Sciences, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 359-0394, Japan;School of Computer Science, University of Waterloo, 200 University Ave. W, Waterloo, ON, Canada N2L3G1;Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Venue:
Journal of Computer and System Sciences
Year:
2012

Citing 14
Cited 4

On the closest string and substring problems

Journal of the ACM (JACM)
A Linear-Time Algorithm for the 1-Mismatch Problem

WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Banishing Bias from Consensus Sequences

CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Genetic Algorithm Approach for the Closest String Problem

CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Distinguishing string selection problems

Information and Computation
On The Parameterized Intractability Of Motif Search Problems*

Combinatorica
Optimal Solutions for the Closest-String Problem via Integer Programming

INFORMS Journal on Computing
Efficient Algorithms for the Closest String and Distinguishing String Selection Problems

FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Closest Substring Problems with Small Distances

SIAM Journal on Computing
Complexities of the centre and median string problems

CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
More Efficient Algorithms for Closest String and Substring Problems

SIAM Journal on Computing
Fast Exact Algorithms for the Closest String and Substring Problems with Application to the Planted (L,d)-Motif Model

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Space and time efficient algorithms for planted motif search

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Parameterized Complexity

Parameterized Complexity

The parameterized complexity of the shared center problem

CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Enumerating neighbour and closest strings

IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
An efficient two-phase ant colony optimization algorithm for the closest string problem

SEAL'12 Proceedings of the 9th international conference on Simulated Evolution and Learning
On approximating string selection problems with outliers

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a set of n strings of length L and a radius d, the closest string problem (CSP for short) asks for a string t"s"o"l that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization version admits a polynomial time approximation scheme (PTAS). Parameterized algorithms have been then developed to solve the problem when d is small. In this paper, with a new approach (called the 3-string approach), we first design a parameterized algorithm for binary strings that runs in O(nL+nd^3@?6.731^d) time, while the previous best runs in O(nL+nd@?8^d) time. We then extend the algorithm to arbitrary alphabet sizes, obtaining an algorithm that runs in time O(nL+nd@?(1.612(|@S|+@b^2+@b-2))^d), where |@S| is the alphabet size and @b=@a^2+1-2@a^-^1+@a^-^2 with @a=|@S|-1+13. This new time bound is better than the previous best for small alphabets, including the very important case where |@S|=4 (i.e., the case of DNA strings).