New complexity results for the k-covers problem

Authors:
Costas S. Iliopoulos;Manal Mohamed;W. F. Smyth
Affiliations:
Algorithm Design Group, Department of Computer Science, King's College London, London WC2R 2LS, UK and Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth WA 6845, Austr ...;Algorithm Design Group, Department of Computer Science, King's College London, London WC2R 2LS, UK;Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth WA 6845, Australia and Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, ...
Venue:
Information Sciences: an International Journal
Year:
2011

Citing 12
Cited 4

An O(n log n) algorithm for finding all repetitions in a string

Journal of Algorithms
Detecting leftmost maximal periodicities

Discrete Applied Mathematics - Combinatorics and complexity
Optimal superprimitivity testing for strings

Information Processing Letters
All Highest Scoring Paths in Weighted Grid Graphs and Their Application to Finding All Approximate Repeats in Strings

SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms

The Design and Analysis of Computer Algorithms
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs

SIAM Journal on Computing
Set k-cover algorithms for energy efficient monitoring in wireless sensor networks

Proceedings of the 3rd international symposium on Information processing in sensor networks
Computing all repeats using suffix arrays

Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the 13th Australasian workshop on combinatorial algorithms
Computing the λ-covers of a string

Information Sciences: an International Journal
Algorithms for Computing the λ-regularities in Strings

Fundamenta Informaticae - Workshop on Combinatorial Algorithms
Fast and Practical Algorithms for Computing All the Runs in a String

CPM '07 Proceedings of the 18th annual symposium on Combinatorial Pattern Matching

A linear time algorithm for seeds computation

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The set of parameterized k-covers problem

Theoretical Computer Science
Computing regularities in strings: A survey

European Journal of Combinatorics
Enhanced string covering

Theoretical Computer Science

Quantified Score

Hi-index	0.07

Visualization

Abstract

The k-covers problem (kCP) asks us to compute a minimum cardinality set of strings of given length k1 that covers a given string. It was shown in a recent paper, by reduction to 3-SAT, that the k-covers problem is NP-complete. In this paper we introduce a new problem, that we call the k-bounded relaxed vertex cover problem (RVCP"k), which we show is equivalent to k-bounded set cover (SCP"k). We show further that kCP is a special case of RVCP"k restricted to certain classes G"x","k of graphs that represent all strings x. Thus a minimum k-cover can be approximated to within a factor k in polynomial time. We discuss approximate solutions of kCP, and we state a number of conjectures and open problems related to kCP and G"x","k.