ACM Transactions on Database Systems (TODS)
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Theoretical Computer Science
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Journal of the ACM (JACM)
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
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SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
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Journal of the ACM (JACM)
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SIAM Journal on Computing
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ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
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Journal of the ACM (JACM)
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
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CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Improved Approximation Results on the Shortest Common Supersequence Problem
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IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
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SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Approximation Algorithms
Memetic algorithms with partial lamarckism for the shortest common supersequence problem
IWINAC'05 Proceedings of the First international work-conference on the Interplay Between Natural and Artificial Computation conference on Artificial Intelligence and Knowledge Engineering Applications: a bioinspired approach - Volume Part II
Weighted shortest common supersequence
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
Restricted and swap common superstring: a parameterized view
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
The constrained shortest common supersequence problem
Journal of Discrete Algorithms
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The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq). In the RCSstr (RCSseq) problem we are given a set S of n strings, s1, s2, ..., sn, and a multiset t = {t1, t2, ..., tm}, and the goal is to find a permutation π : {1,..., m} → {1, ..., m} to maximize the number of strings in S that are substrings (subsequences) of π(t) = tπ(1) tπ(2) ... tπ(m) (we call this ordering of the multiset, π(t), a permutation of t). We first show that in its most general setting the RC-Sstr problem is NP-complete and hard to approximate within a factor of n1-ε, for any ε 0, unless P = NP. Afterwards, we present two separate reductions to show that the RCSstr problem remains NP-Hard even in the case where the elements of t are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the RCSstr problem. In the second part of this paper, we turn to the RCSseq problem, where we present some hardness results, tight lower bounds and approximation algorithms.