On symbolic OBDD-based algorithms for the minimum spanning tree problem

Theoretical Computer Science

Volumn 447, Issue , 2012, Pages 2-12

  Bollig, Beate ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Minimum spanning tree algorithms; Ordered binary decision diagrams; Symbolic algorithms; Transitive closure

Indexed keywords

BLOW-UP; COMMON DYNAMICS; DESIGN AND ANALYSIS; FUNCTIONAL OPERATION; GRAPH PROBLEMS; INPUT GRAPHS; MINIMUM SPANNING TREE PROBLEM; MINIMUM SPANNING TREES; ORDERED BINARY DECISION DIAGRAMS; SYMBOLIC ALGORITHMS; TRANSITIVE CLOSURE;

BOOLEAN FUNCTIONS; DATA STRUCTURES;

ALGORITHMS;

EID: 84863319999     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2011.11.029     Document Type: Conference Paper

References (44)

1. J.L. Balcázar, and A. Lozano The complexity of graph problems for succinctly represented graphs Proc. WG LNCS vol. 411 1989 277 285
2. C.F. Bazlamaçci, and K.S. Hindi Minimum-weight spanning tree algorithms. A survey and empirical study Computers & Operations Research 28 2001 767 785
3. R. Bloem, H.N. Gabow, and F. Somenzi An algorithm for strongly connected component analysis in n log n symbolic steps Proc. FMCAD LNCS vol. 1954 2000 37 54
4. R. Bloem, H.N. Gabow, and F. Somenzi An algorithm for strongly connected component analysis in n log n symbolic steps Formal Methods in System Design 28 2006 37 56
5. B. Bollig On the OBDD complexity of the most significant bit of integer multiplication Proc. TAMC LNCS vol. 4978 2008 306 317
6. B. Bollig Exponential space complexity for OBDD-based reachability analysis Information Processing Letters 110 2010 924 927
7. B. Bollig Exponential space complexity for symbolic maximum flow algorithms in 0-1 networks Proc. MFCS LNCS vol. 6281 2010 186 197
8. B. Bollig, On symbolic representations of maximum matchings and (un)directed graphs, in: Proc. of TCS IFIP AICT 323, 2010, 263-300.
9. B. Bollig, M. Löbbing, M. Sauerhoff, and I. Wegener On the complexity of the hidden weighted bit function for various BDD models Theoretical Informatics and Applications 33 1999 103 115
10. B. Bollig, M. Löbbing, and I. Wegener On the effect of local changes in the variable ordering of ordered decision diagrams Information Processing Letters 59 1996 233 239
11. O. Borůvka, O jistém problému minimální m. Práce Mor. Pirírodoved. Spol. v Brne (Acta Societ. Scient. Natur. Moravicae) 3, 1926, 37-58.
12. Y. Breitbart, H.B. Hunt III, and D.J. Rosenkrantz On the size of binary decision diagrams representing Boolean functions Theoretical Computer Science 145 1995 45 69
13. R.E. Bryant Graph-based algorithms for Boolean function manipulation IEEE Transactions on Computers 35 1986 677 691
14. R.E. Bryant On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication IEEE Trans. on Computers 40 1991 205 213
15. 20 states and beyond Information and Computation 98 1992 142 170
16. B. Chazelle A minimum spanning tree algorithm with inverse-Ackermann type complexity Journal of the ACM 47 6 2000 1028 1047
17. D. Cheriton, and R.E. Tarjan Finding minimum spanning trees SIAM Journal on Computing 5 1976 724 742
18. J. Feigenbaum, S. Kannan, M.V. Vardi, and M. Viswanathan Complexity of problems on graphs represented as OBDDs Proc. STACS LNCS vol. 1373 1998 216 226
19. K. Fisler, and M.Y. Vardi Bisimulation, minimization, and symbolic model checking Formal Methods in System Design 21 1 2002 39 78
20. H. Galperin, and A. Wigderson Succinct representations of graphs Information and Control 56 1983 183 198
21. R. Gentilini, C. Piazza, and A. Policriti Computing strongly connected components in a linear number of symbolic steps Proc. SODA 2003 ACM Press 573 582
22. R. Gentilini, and A. Policriti Biconnectivity on symbolically represented graphs: a linear solution Proc. ISAAC LNCS vol. 2906 2003 554 564
23. R. Gentilini, C. Piazza, and A. Policriti Symbolic graphs: linear solutions to connectivity related problems Algorithmica 50 2008 120 158
24. R.L. Graham, and P. Hell On the history of the minimum spanning tree problem Annals of the History of Computing 7 1985 43 57
25. G.D. Hachtel, and F. Somenzi A symbolic algorithm for maximum flow in 0-1 networks Formal Methods in System Design 10 1997 207 219
26. H. Jin, A. Kuehlmann, and F. Somenzi Fine-grain conjunction scheduling for symbolic reachability analysis Proc. TACAS LNCS vol. 2280 2002 312 326
27. S. Kannan, M. Naor, and S. Rudich Implicit representations of graphs SIAM Journal on Discrete Mathematics 5 1992 596 603
28. D.R. Karger, P.N. Klein, and R.E. Tarjan A randomized linear-time algorithm to find minimum spanning trees Journal of the ACM 42 1995 321 328
29. K. Meer, and D. Rautenbach On the OBDD size for graphs of bounded tree- and clique-width Discrete Mathematics 309 4 2009 843 851
30. R. Nunkesser, and P. Woelfel Representation of graphs by OBDDs Discrete Applied Mathematics 157 2 2009 247 261
31. C.H. Papadimitriou, and M. Yannakakis A note on succinct representations of graphs Information and Control 71 1986 181 185
32. S. Pettie, and V. Ramachandran An optimal minimum spanning tree algorithm Journal of the ACM 49 2002 16 34
33. K. Ravi, R. Bloem, and F. Somenzi A comparative study of symbolic algorithms for the computation of fair cycles Proc. FMCAD LNCS vol. 1954 2000 143 160
34. D. Sawitzki A symbolic approach to the all-pairs shortest-paths problem Proc. WG LNCS vol. 3353 2004 154 167
35. D. Sawitzki Experimental studies of symbolic shortest-path algorithms Proc. WEA LNCS vol. 3059 2004 482 497
36. D. Sawitzki Implicit flow maximization by iterative squaring Proc. SOFSEM LNCS vol. 2932 2004 301 313
37. D. Sawitzki Exponential lower bounds on the space complexity of OBDD-based graph algorithms Proc. LATIN LNCS vol. 3887 2006 781 792
38. D. Sawitzki The complexity of problems on implicitly represented inputs Proc. SOFSEM LNCS vol. 3831 2006 471 482
39. D. Sieling, and I. Wegener NC-algorithms for operations on binary decision diagrams Parallel Processing Letters 48 1993 139 144
40. M. Talamo, and P. Vocca Representing graphs implicitly using almost optimal space Discrete Applied Mathematics 108 2001 193 210
41. I. Wegener Branching Programs and Binary Decision Diagrams - Theory and Applications SIAM Monographs on Discrete Mathematics and Applications 2000
42. P. Woelfel Symbolic topological sorting with OBDDs Proc. MFCS LNCS vol. 2747 2003 671 680
43. P. Woelfel Symbolic topological sorting with OBDDs Journal of Discrete Algorithms 4 1 2006 51 71
44. A. Xie, and P.A. Beerel Implicit enumeration of strongly connected components and an application to formal verification IEEE Transactions on CAD of Integrated Circuits and Systems 19 10 2000 1225 1230