The shortest common nonsubsequence problem is NP-complete
Theoretical Computer Science
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
On the approximation of longest common nonsupersequences and shortest common nonsubsequences
Theoretical Computer Science
On finding minimal, maximal, and consistent sequences over a binary alphabet
Theoretical Computer Science
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
Maximal common subsequences and minimal common supersequences
Information and Computation
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Color Set Size Problem with Application to String Matching
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Optimal suffix tree construction with large alphabets
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximability of constrained LCS
Journal of Computer and System Sciences
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Super-/substring problems and super-/subsequence problems are well-known problems in stringology that have applications in a variety of areas, such as manufacturing systems design and molecular biology. Here we investigate the complexity of a new type of such problem that forms a combination of a super-/substring and a super-/subsequence problem. Moreover we introduce different types of minimal superstring and maximal substring problems. In particular, we consider the following problems: given a set L of strings and a string S, (i) find a minimal superstring (or maximal substring) of L that is also a supersequence (or a subsequence) of S, (ii) find a minimal supersequence (or maximal subsequence) of L that is also a superstring (or a substring) of S. In addition some non-super-/non-substring and non-super-/nonsubsequence variants are studied. We obtain several NP-hardness or even MAX SNP-hardness results and also identify types of "weak minimal" superstrings and "weak maximal" substrings for which (i) is polynomial-time solvable.