Communications of the ACM
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
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
Computational molecular biology
Computational molecular biology
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Approximation algorithms for the shortest common superstring problem
Information and Computation
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
On the wavelength assignment problem in multifiber WDM star and ring networks
IEEE/ACM Transactions on Networking (TON)
An 8/13-approximation algorithm for the asymmetric maximum TSP
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improving table compression with combinatorial optimization
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computing in Science and Engineering
Information Processing Letters
Approximating asymmetric maximum TSP
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
An Approximate Algorithm for the Weighted Hamiltonian Path Completion Problem on a Tree
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
On the Approximation Ratio of the Group-Merge Algorithm for the Shortest Common Suerstring Problem
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Lower Bounds for Approximating Shortest Superstrings over an Alphabet of Size 2
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Diagram processing: computing with diagrams
Artificial Intelligence
Improving table compression with combinatorial optimization
Journal of the ACM (JACM)
An 8/13-approximation algorithm for the asymmetric maximum TSP
Journal of Algorithms
Fast prefix matching of bounded strings
Journal of Experimental Algorithmics (JEA)
Combined super-/substring and super-/subsequence problems
Theoretical Computer Science
The greedy algorithm for shortest superstrings
Information Processing Letters
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
The approximability of the weighted Hamiltonian path completion problem on a tree
Theoretical Computer Science
The Shortest Common Superstring Problem and Viral Genome Compression
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Theoretical Computer Science
Why Greed Works for Shortest Common Superstring Problem
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Minimum-weight cycle covers and their approximability
Discrete Applied Mathematics
Why greed works for shortest common superstring problem
Theoretical Computer Science
The greedy algorithm for shortest superstrings
Information Processing Letters
Minimum-weight cycle covers and their approximability
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Shortest common superstring problem with discrete neural networks
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
Algorithms for three versions of the shortest common superstring problem
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Average case analysis of algorithms
Algorithms and theory of computation handbook
Approximation algorithms for NP-hard optimization problems
Algorithms and theory of computation handbook
On shortest common superstring and swap permutations
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Restricted common superstring and restricted common supersequence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Approximation algorithms for restricted cycle covers based on cycle decompositions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
DNA'06 Proceedings of the 12th international conference on DNA Computing
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The Shortest Common Superstring Problem and Viral Genome Compression
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Restricted and swap common superstring: a parameterized view
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
A probabilistic PTAS for shortest common superstring
Theoretical Computer Science
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We consider the following problem: given a collection of strings s1,…, sm, find the shortest string s such that each si appears as a substring (a consecutive block) of s. Although this problem is known to be NP-hard, a simple greedy procedure appears to do quite well and is routinely used in DNA sequencing and data compression practice, namely: repeatedly merge the pair of (distinct) strings with maximum overlap until only one string remains. Let n denote the length of the optimal superstring. A common conjecture states that the above greedy procedure produces a superstring of length O(n) (in fact, 2n), yet the only previous nontrivial bound known for any polynomial-time algorithm is a recent O(n log n) result.We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n. Furthermore, we present a simple modified version of the greedy algorithm that we show produces a superstring of length at most 3n. We also show the superstring problem to be MAXSNP-hard, which implies that a polynomial-time approximation scheme for this problem is unlikely.