New bounds for the L(h, k) number of regular grids

International Journal of Mobile Network Design and Innovation

Volumn 1, Issue 2, 2006, Pages 92-101

  Calamoneri, Tiziana ^a   Caminiti, Saverio ^a   Fertin, Guillaume ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITÉ DE NANTES   (France)

Author keywords

hexagonal grids; L(h, k) labelling; octagonal grids; squared grids; triangular grids

Indexed keywords

EID: 84901950992     PISSN: 17442869     EISSN: 17442850     Source Type: Journal    
DOI: 10.1504/IJMNDI.2006.010811     Document Type: Article

References (20)

1. Battiti, R., Bertossi, A.A. and Bonuccelli, M.A. (1999) ‘Assigning codes in wireless networks: bounds and scaling properties’, Wireless Networks, Vol. 5, pp.195–209.
2. Bertossi, A.A. and Bonuccelli, M.A. (1995) ‘Code assignment for hidden terminal interference avoidance in multihop packet radio networks’, IEEE/ACM Transactions on Networking, Vol. 3, pp.441–449.
3. Bertossi, A.A., Pinotti, C.M. and Tan, R.B. (2003) ‘Channel assignment with separation for interference avoidance in wireless networks’, IEEE Transactions on Parallel and Distributed Systems, Vol. 14, pp.222–235.
4. Bodlaender, H.L., Kloks, T., Tan, R.B. and van Leeuwen, J. (2000) ‘λ-coloring of graphs’, Proceedings of STACS 2000, LNCS 1770, pp.395–406.
5. Calamoneri, T. (2003) ‘Exact solution of a class of frequency assignment problems in cellular networks and other regular grids’, Proceedings of Eighth Italian Conference on Theoretical Computer Science (ICTCS’03), LNCS 2841, pp.163–173.
6. Calamoneri, T. (2004) ‘The L(h, k)-labelling problem: a survey’, Technical Report 04/2004 University of Rome ‘La Sapienza’, Department of Computer Science.
7. Calamoneri, T. and Petreschi, R. (2004). ‘L(h, 1)-Labelling subclasses of planar graphs’, Journal on Parallel and Distributed Computing, Vol. 64, No. 3, pp.414–426.
8. Chang, G.J., Ke, W-T., Kuo, D., Liu, D.D-F. and Yeh, R.K. (2002) ‘On L(d, 1)-labellings of graphs’, Discrete Mathematics Vol. 220, pp.57–66.
9. Chang, G.J. and Kuo, D. (1996) ‘The L(2, 1)-labelling problem on graphs’, SIAM Journal of Discrete Mathematics, Vol. 9, pp.309–316.
10. Fertin, G. and Raspaud, A. (submitted for publication) ‘L(p, q) labelling of d-dimensional grids’, Discrete Applied Mathematics.
11. Griggs, J.R. and Yeh, R.K. (1992) ‘Labelling graphs with a condition at Distance 2’, SIAM Journal of Discrete Mathematics, Vol. 5, pp.586–595.
12. Hale, W.K. (1980) ‘Frequency assignment: theory and applications’, Proceedings of IEEE, Vol. 68, pp.1497–1514.
13. Jha, P.K., Narayanan, A., Sood, P., Sundaram, K. and Sunder, V. (2000) ‘On L(2, 1)-labelling of the cartesian product of a cycle and a path’, Ars Combinations, Vol. 55, pp.81–89.
14. Jha, PK. (2000) ‘Optimal L(2, 1)-labelling of cartesian products of cycles with an application to independent domination’, IEEE Transactions Circuits and Systems I: Fundamental Theory and Application, Vol. 47, pp.1531–1534.
15. Korže, D. and Vesel, A. (2005) ‘L(2, 1)-labelling of strong products of cycles’, Information Processing Letters, Vol. 94, pp.183–190.
16. Makansi, T. (1987) ‘Transmitter-oriented code assignment for multihop packet radio’, IEEE Transactions on Communications, Vol. 35, No. 12, pp.1379–1382.
17. Metzger, B.H. (1970) ‘Spectrum management technique’, Proceedings of the 38th National ORSA Meeting, LNCS 1770, pp.395–406.
18. Molloy, M. and Salavatipour, M.R. (2002) ‘Frequency channel assignment on planar networks’, Proceedings of Tenth Annual European Symposium on Algorithms (ESA), LNCS 2461, pp.736–747.
19. Sakai, D. (1994) ‘Labelling chordal graphs: distance two condition’, SIAM Journal of Discrete Mathematics, Vol. 7, pp.133–140.
20. n and related graphs’, SIAM Journal of Discrete Mathematics, Vol. 8, pp.499–506.