A general approach to L(h,k)-label interconnection networks

Journal of Computer Science and Technology

Volumn 23, Issue 4, 2008, Pages 652-659

  Calamoneri, Tiziana ^a   Caminiti, Saverio ^a   Petreschi, Rossella ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Channel assignment problem; L(h, k) labeling; Multistage interconnection network

Indexed keywords

ADJACENT NODES; CCC NETWORKS; CHANNEL ASSIGNMENT PROBLEM; GENERAL APPROACH; GRAPH G; INTERCONNECTION NETWORKS; INTERCONNECTION TOPOLOGIES; L(H, K)-LABELING; L-LABELING; MULTISTAGE INTERCONNECTION NETWORK; NEW CLASS; NON-NEGATIVE INTEGERS; NP-COMPLETE; OF GRAPHS;

COLOR; GRAPH THEORY; NUCLEAR PROPULSION; OPTICAL PROPERTIES; TOPOLOGY;

LABELING;

EID: 49449097220     PISSN: 10009000     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11390-008-9161-8     Document Type: Article

References (27)

1. Roberts F S. From Garbage to Rainbows: Generalizations of Graph Coloring and Their Applications. Graph Theory, Combinatorics, and Applications, 2, Alavi Y, Chartrand G, Oellermann O R, Schwenk A J (eds.), 2, New York: Wiley, 1991, pp.1031-1052.
2. Jensen T R, Toft B. Graph Coloring Problems. New York: John Wiley & Sons, 1995.
3. Griggs J R, Yeh R K. Labeling graphs with a condition at distance 2. SIAM Journal on Discrete Mathematics 1992, 5(4): 586-595.
4. Georges J P, Mauro D W. Generalized vertex labelings with a condition at distance two. Congressus Numerantium, 1995, 109: 141-159.
5. Calamoneri T. Exact solution of a class of frequency assignment problems in cellular networks. Discrete Mathematics & Theoretical Computer Science, 2006, 8: 141-158.
6. Calamoneri T, Pelc A, Petreschi R: Labeling trees with a condition at distance two. Discrete Mathematics, 2006, 306(14): 1534-1539.
7. Georges J P, Mauro D W. Labeling trees with a condition at distance two. Discrete Mathematics, 2003, 269(1-3): 127-148.
8. Georges J P, Mauro D W, Stein M I. Labeling products of complete graphs with a condition at distance two. SIAM Journal on Discrete Mathematics, 2001, 14(1): 28-35.
9. J van den Heuvel, R A Leese, M A Shepherd. Graph labelling and radio channel assignment. Journal of Graph Theory, 1998, 29(4): 263-283.
10. Agnarsson G, Halldórsson M M. Coloring powers of planar graphs. SIAM Journal on Discrete Mathematics, 2003, 16(4): 651-662.
11. Hale W K. Frequency assignment: Theory and application. Proceedings of the IEEE, 1980, 68(12): 1487-1514.
12. K I Aardal, S P M van Hoesel, A M C A Koster, C Mannino, A Sassano. Models and solution techniques for frequency assignment problems. ZIB-Report 01-40, Konrad-Zuse-Zentrum fur Informationstechnik Berlin, 2001.
13. H L Bodlaender, T Kloks, R B Tan, J van Leeuwen. Lambda coloring of graphs. In Proc. 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2000), Lille, France, LNCS 1770, Feb. 2000, pp.395-406.
14. Calamoneri T, Petreschi R. L(2, 1)-labeling of planar graphs. Journal on Parallel and Distributed Computing, 2004, 64(3): 414-426.
15. Calamoneri T, Petreschi R. λ-coloring matrogenic graphs. Discrete Applied Mathematics, 2006, 154: 2445-2457.
16. Chang G J, Kuo D. The L(2, 1)-labeling problem on graphs. SIAM Journal on Discrete Mathematics, 1996, 9: 309-316.
17. Fiala J, Kloks T, Kratochvíl J. Fixed-parameter complexity of λ-colorings. In Proc. Graph Theoretic Concepts in Computer Science (WG'99), LNCS 1665, 1999, pp.350-363.
18. Murphey R A, Pardalos P M, Resende M G C. Frequency Assignment Problems. Handbook of Combinatorial Optimization, Du D-Z, Pardalos P M (eds.), Kluwer Academic Publishers, 1999, pp.295-377.
19. Sakai D. Labeling chordal graphs: Distance 2 condition. SIAM Journal on Discrete Mathematics, 1994, 7(1): 133-140.
20. Shepherd M. Radio channel assignment [Dissertation]. Merton College, Oxford, 1998.
21. n and related graphs. SIAM Journal on Discrete Mathematics, 1995, 8(4): 499-506.
22. Calamoneri T. The L(h, k)-labelling problem: A survey and annotated bibliography. The Computer Journal, 2006, 49(5): 585-608, http://www.dsi. uniroma1.it/~calamo/survey.html.
23. Leighton F T. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, 1992.
24. Preparata F P, Vuillemin J. The cube-connected cycles: A versatile network for parallel computation. Communications of ACM, 1981, 24(5): 300-309.
25. Calamoneri T, Massini A. Efficient algorithms for checking the equivalence of multistage interconnection networks. Journal on Parallel and Distributed Computing, 2004, 64(1): 135-150.
26. Calamoneri T, Petreschi R. A new 3D representation of trivalent Cayley networks. Information Processing Letters, 1997, 61(5): 247-252.
27. Vadapalli P, Srimani P K. Trivalent Cayley graphs for interconnection networks. Information Processing Letters, 1995, 54(6): 329-335.