Data compression: methods and theory
Data compression: methods and theory
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
The greedy algorithm for shortest superstrings
Information Processing Letters
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 Smoothed Complexity of Edit Distance
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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
A probabilistic PTAS for shortest common superstring
Theoretical Computer Science
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The shortest common superstring problem (SCS) has been extensively studied for its applications in string compression and DNA sequence assembly. Although the problem is known to be Max-SNP hard, the simple greedy algorithm performs extremely well in practice. To explain the good performance, previous researchers proved that the greedy algorithm is asymptotically optimal on random instances. Unfortunately, the practical instances in DNA sequence assembly are very different from the random instances. In this paper we explain the good performance of the greedy algorithm by using the smoothed analysis. We show that, for any given instance I of SCS, the average approximation ratio of the greedy algorithm on a small random perturbation of I is 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 the worst case SCSW cannot be approximated within the ratio n^1^/^7^-^@e, while the greedy algorithm still has 1+o(1) smoothed approximation ratio.