A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations
- 198 Downloads
In this paper a fast greedy sequential heuristic for the vertex colouring problem is presented. The suggested algorithm builds the same colouring of the graph as the well-known greedy sequential heuristic in which on every step the current vertex is coloured in the minimum possible colour. Our main contributions include introduction of a special matrix of forbidden colours and application of efficient bitwise operations on bit representations of the adjacency and forbidden colours matrices. Computational experiments show that in comparison with the classical greedy heuristic the average speedup of the developed approach is 2.6 times on DIMACS instances.
KeywordsGraph colouring Heuristic Bitwise operations Greedy algorithm Sequential colouring
The work is conducted at National Research University Higher School of Economics and supported by RSF Grant 14-41-00039.
- Erciyes K (2013) Vertex coloring. In: distributed graph algorithms for computer networks, pp 107–134Google Scholar
- Johnson DS (1974) Worst case behavior of graph coloring algorithms. In: Proceedings of the Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing. Utilitas Mathematica Publishing, pp 513–528Google Scholar
- Kosowski A, Manuszewski K (2004) Classical coloring of graphs. In: Kubale M (ed) Graph colorings. AMS Contemporary Mathematics, pp 1–20Google Scholar
- Matula DM, Marble BG, Isaacson JD (1972) Graph coloring algorithms. In: Graph theory and computing. Academic Press, New York, pp 109–122Google Scholar
- Meirong X, Yuzhen W (2014) T-coloring of graphs with application to frequency assignment in cellular mobile networks. In: Proceedings of the 33rd Chinese Control Conference (CCC), 2014Google Scholar
- Odaira R, Nakaike T, Inagaki T, Komatsu H, Nakatani T (2010) Coloring-based coalescing for graph coloring register allocation. In: CGO ’10: Proceedings of the 8th annual IEEE/ACM international symposium on Code generation and optimizationGoogle Scholar
- Pardalos PM, Mavridou T, Xue J (1999) The graph coloring problem: a bibliographic survey. In: Du DZ, Pardalos PM (ed) Handbook of combinatorial optimization, pp 1077–1141Google Scholar
- Radin A (2000) Graph coloring heuristics from investigation of smallest hard to color graphs. MS Thesis, Rochester Institute of TechnologyGoogle Scholar
- Smith MD, Ramsey N, Holloway G (2004) A generalized algorithm for graph-coloring register allocation. In: PLDI ’04: Proceedings of the ACM SIGPLAN 2004 Conference on Programming language design and implementationGoogle Scholar
- Wang H, Alidaee B, Kochenberger GA (2004) Evaluating a clique partitioning problem model for clustering high-dimensional data mining. In: Proceedings of the 10th Americas Conference on Information Systems (AMCIS 2004), New York, NY, 6–8 August 2004Google Scholar