Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor
An optimal algorithm for the k-fixed-endpoint path cover on proper interval graphs
Mertzios, G.B.; Unger, W.
Authors
W. Unger
Abstract
In this paper we consider the k-fixed-endpoint path cover problem on proper interval graphs, which is a generalization of the path cover problem. Given a graph G and a set T of k vertices, a k-fixed-endpoint path cover of G with respect to T is a set of vertex-disjoint simple paths that covers the vertices of G, such that the vertices of T are all endpoints of these paths. The goal is to compute a k-fixed-endpoint path cover of G with minimum cardinality. We propose an optimal algorithm for this problem with runtime O(n), where n is the number of intervals in G. This algorithm is based on the Stair Normal Interval Representation (SNIR) matrix that characterizes proper interval graphs. In this characterization, every maximal clique of the graph is represented by one matrix element; the proposed algorithm uses this structural property, in order to determine directly the paths in an optimal solution.
Citation
Mertzios, G., & Unger, W. (2010). An optimal algorithm for the k-fixed-endpoint path cover on proper interval graphs. Mathematics in Computer Science, 3(1), 85-96. https://doi.org/10.1007/s11786-009-0004-y
Journal Article Type | Article |
---|---|
Publication Date | Mar 1, 2010 |
Deposit Date | Dec 8, 2011 |
Publicly Available Date | Jan 10, 2012 |
Journal | Mathematics in Computer Science |
Print ISSN | 1661-8270 |
Electronic ISSN | 1661-8289 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 3 |
Issue | 1 |
Pages | 85-96 |
DOI | https://doi.org/10.1007/s11786-009-0004-y |
Keywords | Proper interval graph, Perfect graph, Path cover, SNIR matrix, Linear-time algorithm. |
Files
Accepted Journal Article
(229 Kb)
PDF
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s11786-009-0004-y.
You might also like
Graphs with minimum fractional domatic number
(2023)
Journal Article
Approximate and Randomized algorithms for Computing a Second Hamiltonian Cycle
(2023)
Journal Article
Sliding into the Future: Investigating Sliding Windows in Temporal Graphs
(2023)
Conference Proceeding
Fast parameterized preprocessing for polynomial-time solvable graph problems
(2023)
Journal Article
The complexity of computing optimum labelings for temporal connectivity
(2022)
Conference Proceeding
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search