A greedy approximation algorithm for constructing shortest common superstrings
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
Approximation algorithms for the shortest common superstring problem
Information and Computation
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
Rotations of periodic strings and short superstrings
Journal of Algorithms
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
An Algorithm for Reconstructing Protein and RNA Sequences
Journal of the ACM (JACM)
\boldmath A $2\frac12$-Approximation Algorithm for Shortest Superstring
SIAM Journal on Computing
A 2 2/3-Approximation Algorithm for the Shortest Superstring Problem
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
An Experimental Comparison of Approximation Algorithms for the Shortest Common Superstring Problem
ENC '04 Proceedings of the Fifth Mexican International Conference in Computer Science
Towards a DNA sequencing theory (learning a string)
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Approximating shortest superstrings
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
The greedy algorithm for shortest superstrings
Information Processing Letters
Explicit inapproximability bounds for the shortest superstring problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
IEEE Transactions on Information Theory
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Why large CLOSEST STRING instances are easy to solve in practice
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
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
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The shortest common superstring problem (SCS) has been widely studied for its applications in string compression and DNA sequence assembly. Although it is known to be Max-SNP hard, the simple greedy algorithm works extremely well in practice. Previous researchers have proved that the greedy algorithm is asymptotically optimal on random instances. Unfortunately, the practical instances in DNA sequence assembly are very different from random instances.In this paper we explain the good performance of greedy algorithm by using the smoothed analysis. We show that, for anygiven instance Iof SCS, the average approximation ratio of the greedy algorithm on a small random perturbation of Iis 1 + o(1). The perturbation defined in the paper is small and naturally represents the mutations of the DNA sequence during evolution.Due to the existence of the uncertain nucleotides in the output of a DNA sequencing machine, we also proposed the shortest common superstring with wildcards problem (SCSW). We prove that in worst case SCSW cannot be approximated within ratio n1/7 茂戮驴 茂戮驴, while the greedy algorithm still has 1 + o(1) smoothed approximation ratio.