Complementary Graph Coloring
The objective of the Graph Coloring problem is to color vertices of a graph in such a way that no two vertices that share an edge are assigned the same color. Aircraft Scheduling, Frequency Assignment, register allocation are all real life applications that can be solved using graph coloring. Graph Coloring is a well-known NP-complete problem to the academia in computer science and mathematics. In this paper we use the concept of complementary graphs to come up with a new heuristic for graph coloring. Our results are compared with an exact algorithm and other heuristic algorithms to evaluate our algorithm’s performance.
D. Br ́elaz. New methods to color the vertices of a graph. Communications of the ACM, 22(4):251–256, 1979.
M. R. Garey and D. S. Johnson. Computers and intractibility: a guide to the theory of np-completeness. WH Freeman and Company, New York, 18:41, 1979.
M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified np-complete problems. In Proceedings of the sixth annual ACM symposium on Theory of computing, pages 47–63. ACM, 1974.
E. L. Lawler. A note on the complexity of the chromatic number problem. Information Processing Letters, 5(3):66–67, 1976.
P. San Segundo. A new dsatur-based algorithm for exact vertex coloring. Computers & Operations Research, 39(7):1724–1733, 2012.
E. Sewell. An improved algorithm for exact graph coloring. DIMACS series in discrete mathematics and theoretical computer science, 26:359–373, 1996.
G. M. Slota, S. Rajamanickam, and K. Madduri. Bfs and coloring-based parallel algorithms for strongly connected components and related problems. In IEEE International Parallel and Distributed Processing Symposium, 2014.
D. J. Welsh and M. B. Powell. An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer Journal, 10(1):85–86, 1967.
Authors who submit papers with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- By submitting the processing fee, it is understood that the author has agreed to our terms and conditions which may change from time to time without any notice.
- It should be clear for authors that the Editor In Chief is responsible for the final decision about the submitted papers; have the right to accept\reject any paper. The Editor In Chief will choose any option from the following to review the submitted papers:A. send the paper to two reviewers, if the results were negative by one reviewer and positive by the other one; then the editor may send the paper for third reviewer or he take immediately the final decision by accepting\rejecting the paper. The Editor In Chief will ask the selected reviewers to present the results within 7 working days, if they were unable to complete the review within the agreed period then the editor have the right to resend the papers for new reviewers using the same procedure. If the Editor In Chief was not able to find suitable reviewers for certain papers then he have the right to reject the paper.
- Author will take the responsibility what so ever if any copyright infringement or any other violation of any law is done by publishing the research work by the author
- Before publishing, author must check whether this journal is accepted by his employer, or any authority he intends to submit his research work. we will not be responsible in this matter.
- If at any time, due to any legal reason, if the journal stops accepting manuscripts or could not publish already accepted manuscripts, we will have the right to cancel all or any one of the manuscripts without any compensation or returning back any kind of processing cost.
- The cost covered in the publication fees is only for online publication of a single manuscript.