Approximating the L(h, k)-labelling problem

International Journal of Mobile Network Design and Innovation

Volumn 1, Issue 2, 2006, Pages 113-117

  Halldórsson, Magnús M ^a  

^a UNIVERSITY OF ICELAND   (Iceland)

Author keywords

approximation algorithms; distance constrained colouring; frequency allocation; L(h, k) labelling

Indexed keywords

EID: 79955642499     PISSN: 17442869     EISSN: 17442850     Source Type: Journal    
DOI: 10.1504/IJMNDI.2006.010813     Document Type: Article

References (9)

1. Agnarsson, G., Greenlaw, R. and Halldórsson, M.M. (2000), ‘On powers of chordal graphs and their colorings’, Congressus Numerantium, pp.142–147.
2. Agnarsson, G. and Halldórsson, M.M. (2003) ‘Colouring powers of planar graphs’, SIAM Journal of Discrete Mathematics, Vol. 16, No. 4, pp.651–662.
3. Calamoneri, T. (2004) ‘The L(h, k)-labelling problem: a survey’, Technical Report 04/2004, Department of Computer Science, University of Rome “La Sapienza”, 8 November, Available at: http://www.dsi.uniromaLit/calamo/survey.html.
4. Calamoneri, T. and Vocca, P. (2005) ‘On the L(h,k)-labelling problem of bipartite graphs’, Proceedings of 12th Colloquium on Structural Information and Communication Complexity (SIROCCO 2005), Lecture Notes in Computer Science 3499, pp.65–77.
5. Feige, U. and Kilian, J. (1998) ‘Zero knowledge and the chromatic number’, Journal of Computer and System Sciences, Vol. 57, pp.187–199.
6. Griggs, J.R. and Yeh, R.K. (1992) ‘Labelling graphs with a condition at distance 2’, SIAM Journal of Discrete Mathematics, Vol. 5, No. 4, pp.586–595.
7. Halldórsson, M.M. (2005) ‘A still better performance guarantee for approximate graph coloring', Information Processing Letters, Vol. 45, 25 January, pp.19–23.
8. McCormick, S.T. (1983) ‘Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem’, Mathematical Programming, Vol. 26, No. 2, pp.153–171.
9. Note that the span is frequently defined to be simply the largest colour used. Our definition matches the size of the colour palette used including the ‘holes’. The difference is not significant for the approximation results presented here.