Data compression: methods and theory
Data compression: methods and theory
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
\boldmath A $2\frac12$-Approximation Algorithm for Shortest Superstring
SIAM Journal on Computing
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
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On problems without polynomial kernels
Journal of Computer and System Sciences
Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology
Combinatorial Algorithms
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
On shortest common superstring and swap permutations
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Restricted common superstring and restricted common supersequence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Explicit inapproximability bounds for the shortest superstring problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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In several areas, in particular in bioinformatics and in AI planning, Shortest Common Superstring problem (SCS) and variants thereof have been successfully applied. In this paper we consider two variants of SCS recently introduced (Restricted Common Superstring, $\ensuremath{\text{\textsc{RCS}}}$) and (Swapped Common Superstring, $\ensuremath{\text{\textsc{SWCS}}}$). In $\ensuremath{\text{\textsc{RCS}}}$ we are given a set S of strings and a multiset, and we look for an ordering $\mathcal{M}_o$ of $\mathcal{M}$ such that the number of input strings which are substrings of $\mathcal{M}_o$ is maximized. In $\ensuremath{\text{\textsc{SWCS}}}$ we are given a set S of strings and a text $\mathcal{T}$, and we look for a swap ordering $\mathcal{T}_o$ of $\mathcal{T}$ (an ordering of $\mathcal{T}$ obtained by swapping only some pairs of adjacent characters) such that the number of input strings which are substrings of $\mathcal{T}_o$ is maximized. In this paper we investigate the parameterized complexity of the two problems. We give two fixed-parameter algorithms, where the parameter is the size of the solution, for $\ensuremath{\text{\textsc{SWCS}}}$ and $\ensuremath{\text{\textsc{$\ell$-RCS}}} $ (the $\ensuremath{\text{\textsc{RCS}}}$ problem restricted to strings of length bounded by a parameter ℓ). Furthermore, we complement these results by showing that $\ensuremath{\text{\textsc{SWCS}}}$ and $\ensuremath{\text{\textsc{$\ell$-RCS}}} $ do not admit a polynomial kernel.