Geometric representation of graphs in low dimension using axis parallel boxes

Algorithmica (New York)

Volumn 56, Issue 2, 2010, Pages 129-140

  Chandran, L Sunil ^a   Francis, Mathew C ^a   Sivadasan, Naveen ^b  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b TATA CONSULTANCY SERVICES   (India)

Author keywords

Boxicity; Derandomization; Intersection graphs; Random graph; Randomized algorithm

Indexed keywords

BOXICITY; DERANDOMIZATION; INTERSECTION GRAPH; RANDOM GRAPHS; RANDOMIZED ALGORITHMS;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; SET THEORY;

POLYNOMIAL APPROXIMATION;

EID: 74849121431     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-008-9163-5     Document Type: Article

References (25)

1. P.K. Agarwal M. van Kreveld S. Suri 1998 Label placement by maximum independent set in rectangles Comput. Geom. Theory Appl. 11 209 218 0921.68100
2. D. Angluin L.G. Valiant 1979 Fast probabilistic algorithms for Hamiltonian circuits and matchings J. Comput. Syst. Sci. 18 155 193 0437.05040 10.1016/0022-0000(79)90045-X 532174 (Pubitemid 9461409)
3. S. Bellantoni I.B.-A. Hartman T. Przytycka S. Whitesides 1993 Grid intersection graphs and boxicity Discrete Math. 114 41 49 0784.05031 10.1016/0012-365X(93)90354-V 1217740
4. P. Berman B. DasGupta S. Muthukrishnan S. Ramaswami 2001 Efficient approximation algorithms for tiling and packing problems with rectangles J. Algorithms 41 443 470 0999.68248 10.1006/jagm.2001.1188 1869262 (Pubitemid 33665551)
5. H.L. Bodlaender 1993 A tourist guide through treewidth Acta Cybern. 11 1 21 0804.68101 1268488
6. Bollobás, B.: Random Graphs, 2 edn. Cambridge University Press, Cambridge (2001)
7. T.M. Chan 2003 Polynomial-time approximation schemes for packing and piercing fat objects J. Algorithms 46 178 189 1030.68093 10.1016/S0196-6774(02) 00294-8 1969718
8. L.S. Chandran N. Sivadasan 2007 Boxicity and Treewidth J. Comb. Theory Ser. B 97 5 733 744 1121.05091 10.1016/j.jctb.2006.12.004 2344136
9. L.S. Chandran M.C. Francis N. Sivadasan 2007 Boxicity and maximum degree J. Comb. Theory Ser. B 10.1016/j.jctb.2007.08.002
10. Chandran, L.S., Francis, M.C., Sivadasan, N.: Geometric representation of graphs in low dimension using axis parallel boxes. Technical report available at http://arxiv.org/pdf/cs/0605013
11. Chang, Y.W., West, D.B.: Rectangle number for hyper cubes and complete multipartite graphs. In: 29th SE Conf. Comb., Graph Th. and Comp., Congr. Numer., vol. 132, pp. 19-28 (1998)
12. Chang, Y.W., West, D.B.: Interval number and boxicity of digraphs. In: Proceedings of the 8th International Graph Theory Conf. (1998)
13. Cozzens, M.B.: Higher and multidimensional analogues of interval graphs. Ph.D. thesis, Rutgers University, New Brunswick, NJ (1981)
14. T. Erlebach K. Jansen E. Seidel 2005 Polynomial-time approximation schemes for geometric intersection graphs SIAM J. Comput. 34 1302 1323 1081.68031 10.1137/S0097539702402676 2165741 (Pubitemid 43003142)
15. R.B. Feinberg 1979 The circular dimension of a graph Discrete Math. 25 27 31 0392.05057 10.1016/0012-365X(79)90149-3 522744
16. 1-ε Acta Math. 182 105 142 10.1007/BF02392825 1687331
17. Kloks, T.: Treewidth: Computations and Approximations. Lecture Notes in Computer Science, vol. 842. Springer, Berlin (1994)
18. J. Kratochvil 1994 A special planar satisfiability problem and a consequence of its NP-completeness Discrete Appl. Math. 52 233 252 0810.68083 10.1016/0166-218X(94)90143-0 1287974
19. Roberts, F.S.: On the boxicity and Cubicity of a graph. In: Recent Progresses in Combinatorics, pp. 301-310. Academic, New York (1969)
20. B. Rosgen L. Stewart 2007 Complexity results on graphs with few cliques Discrete Math. Theor. Comput. Sci. 9 127 136 1153.05333 2335890
21. Scheinerman, E.R.: Intersection classes and multiple intersection parameters. Ph.D. thesis, Princeton University (1984)
22. J.B. Shearer 1980 A note on circular dimension Discrete Math. 29 103 103 0437.05049 10.1016/0012-365X(90)90290-X 553653
23. C. Thomassen 1986 Interval representations of planar graphs J. Comb. Theory Ser. B 40 9 20 0595.05027 10.1016/0095-8956(86)90061-4 830590
24. W.T. Trotter J.D.B. West 1987 Poset boxicity of graphs Discrete Math. 64 105 107 0646.05064 10.1016/0012-365X(87)90247-0 882619
25. M. Yannakakis 1982 The complexity of the partial order dimension problem SIAM J. Algebraic Discrete Methods 3 351 358 0516.06001 10.1137/0603036 666860