Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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
The Closest Substring problem with small distances
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
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
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
The bounded search tree algorithm for the closest string problem has quadratic smoothed complexity
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
| Hi-index | 0.00 |
Given a set of n strings of length L and a radius d, the closest string problem asks for a new string tsol 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 + nd36.731d) time, while the previous best runs in O(nL + nd8d) time. We then extend the algorithm to arbitrary alphabet sizes, obtaining an algorithm that runs in O(nL + nd1.612d(α2 + 1 - 2α-1 + α-2)3d time, where α = 3√√|Σ| - 1 + 1. This new time bound is better than the previous best for small alphabets, including the very important case where |Σ| = 4 (i.e., the case of DNA strings).