Version 1
: Received: 15 November 2019 / Approved: 20 November 2019 / Online: 20 November 2019 (02:19:01 CET)
How to cite:
Badr, E.M.; Aloufi, K. An Exact Parallel Algorithm for the Radio k-coloring Problem. Preprints2019, 2019110232. https://doi.org/10.20944/preprints201911.0232.v1
Badr, E.M.; Aloufi, K. An Exact Parallel Algorithm for the Radio k-coloring Problem. Preprints 2019, 2019110232. https://doi.org/10.20944/preprints201911.0232.v1
Badr, E.M.; Aloufi, K. An Exact Parallel Algorithm for the Radio k-coloring Problem. Preprints2019, 2019110232. https://doi.org/10.20944/preprints201911.0232.v1
APA Style
Badr, E.M., & Aloufi, K. (2019). An Exact Parallel Algorithm for the Radio <em>k</em>-coloring Problem. Preprints. https://doi.org/10.20944/preprints201911.0232.v1
Chicago/Turabian Style
Badr, E.M. and Khalid Aloufi. 2019 "An Exact Parallel Algorithm for the Radio <em>k</em>-coloring Problem" Preprints. https://doi.org/10.20944/preprints201911.0232.v1
Abstract
For a positive integer k, a radio k-coloring of a simple connected graph G = (V (G), E(G)) is a mapping | f(u) - f(v)| ≥ k +1-d (u , v ) such that f :V (G)→{0,1, 2,...} for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer it assigns to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this work, we propose four algorithms (two serial algorithms and their parallel versions) which related to the radio k-coloring problem. One of them is an approximate algorithm that determines an upper bound of the radio number of a given graph. The other is an exact algorithm which finds the radio number of a graph G. The approximate algorithm is a polynomial time algorithm while the exact algorithm is an exponential time algorithm. The parallel algorithms are parallelized using the Message Passing Interface (MPI) standard. The experimental results prove the ability of the proposed algorithms to achieve a speedup 7 for 8 processors.
Keywords
radio k-coloring; radio number; MPI; parallel algorithm
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
