Dynamic algorithms for graphs of bounded treewidth

Algorithmica (New York)

Volumn 27, Issue 3-4, 2000, Pages 292-315

  Hagerup, T ^a,b  

^a GOETHE UNIVERSITY   (Germany)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Dynamic algorithms; Graph algorithms; Monadic second order logic; Path queries; Treewidth

Indexed keywords

EID: 0041480795     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004530010021     Document Type: Article

References (33)

1. N. Alon and B. Schieber, Optimal preprocessing for answering on-line product queries, Tech. Rep. No. 71/87, Tel Aviv University, 1987.
2. S. R. Arikati, S. Chaudhuri, and C. D. Zaroliagis, All-pairs min-cut in sparse networks, in Proc. 15th Conference on Foundations of Software Technology and Theoretical Computer Science (P. S. Thiagarajan, ed.), Lecture Notes in Computer Science, Vol. 1026, Springer-Verlag, Berlin, 1995, pp. 363-376.
3. S. Arnborg, J. Lagergren, and D. Seese, Easy problems for tree-decomposable graphs, J. Algorithms, 12 (1991), 308-340.
4. M. W. Bern, E. L. Lawler, and A. L. Wong, Linear-time computation of optimal subgraphs of decomposable graphs, J. Algorithms, 8 (1987), 216-235.
5. H. L. Bodlaender, Dynamic programming on graphs with bounded treewidth, in Proc. 15th International Colloquium on Automata, Languages and Programming (T. Lepistö and A. Salomaa, eds.), Lecture Notes in Computer Science, Vol. 317, Springer-Verlag, Berlin, 1988, pp. 105-118.
6. H. L. Bodlaender, NC algorithms for graphs with small treewidth, in Proc. 14th International Workshop on Graph-Theoretic Concepts in Computer Science (J. van Leeuwen, ed.), Lecture Notes in Computer Science, Vol. 344, Springer-Verlag, Berlin, 1989, pp. 1-10.
7. H. L. Bodlaender, On reduction algorithms for graphs with small treewidth, in Proc. 19th International Workshop on Graph-Theoretic Concepts in Computer Science (J. van Leeuwen, ed.), Lecture Notes in Computer Science, Vol. 790, Springer-Verlag, Berlin, 1994, pp. 45-56.
8. H. L. Bodlaender, Dynamic algorithms for graphs with treewidth 2, in Proc. 19th International Workshop on Graph-Theoretic Concepts in Computer Science (J. van Leeuwen, ed.), Lecture Notes in Computer Science, Vol. 790, Springer-Verlag, Berlin, 1994, pp. 112-124.
9. H. L. Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput., 25 (1996), 1305-1317.
10. H. L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theoret. Comput. Sci., 209 (1998), 1-45.
11. H. L. Bodlaender and T. Hagerup, Parallel algorithms with optimal speedup for bounded treewidth, SIAM J. Comput., 27 (1998), 1725-1746.
12. R. B. Bone, R. G. Parker, and C. A. Tovey, Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families, Algorithmica, 7 (1992), 555-581.
13. S. Chaudhuri and C. D. Zaroliagis, Shortest path queries in digraphs of small treewidth, in Proc. 22nd International Colloquium on Automata, Languages and Programming (Z. Fülöp and F. Gécseg, eds.), Lecture Notes in Computer Science, Vol. 944, Springer-Verlag, Berlin, 1995, pp. 244-255.
14. S. Chaudhuri and C. D. Zaroliagis, Shortest paths in digraphs of small treewidth. Part II: Optimal parallel algorithms, Theoret. Comput. Sci., 203 (1998), 205-223.
15. B. Chazelle, Computing on a free tree via complexity-preserving mappings, Algorithmica, 2 (1987), 337-361.
16. R. F. Cohen, S. Sairam, R. Tamassia, and J. S. Vitter, Dynamic algorithms for optimization problems in bounded tree-width graphs, in Proc. 3rd Integer Programming and Combinatorial Optimization Conference (G. Rinaldi and L. A. Wolsey, eds.), Ciaco, Louvain-la-Neuve, 1993, pp. 99-112.
17. R. Cole and U. Vishkin, Deterministic coin tossing with applications to optimal parallel list ranking, Inform. and Control, 70 (1986), 32-53.
18. B. Courcelle, Graph rewriting: an algebraic and logic approach, in Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics (J. van Leeuwen, ed.), Elsevier, Amsterdam and The MIT Press, Cambridge, MA, 1990, Chap. 5, pp. 193-242.
19. B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Inform. and Comput., 85 (1990), 12-75.
20. B. Courcelle and M. Mosbah, Monadic second-order evaluations on tree-decomposable graphs, Theoret. Comput. Sci., 109 (1993), 49-82.
21. G. N. Frederickson, Maintaining regular properties dynamically in k-terminal graphs, Preprint, 1995.
22. A. Habel, H.-J. Kreowski, and W. Vogler, Decidable boundedness problems for sets of graphs generated by hyperedge-replacement, Theoret. Comput. Sci., 89 (1991), 33-62.
23. T. Hagerup, Parallel preprocessing for path queries without concurrent reading, Inform. and Comput., to appear.
24. D. Harel and R. E. Tarjan, Fast algorithms for finding nearest common ancestors, SIAM J. Comput., 13 (1984), 338-355.
25. J. JáJá, An Introduction to Parallel Algorithms, Addison-Wesley, Reading, MA, 1992.
26. W. Paul, U. Vishkin, and H. Wagener, Parallel computation on 2-3-trees, RAIRO Theoret. informatics, 17 (1983), 397-404.
27. V. Radhakrishnan, H. B. Hunt III, and R. E. Stearns, Efficient algorithms for solving systems of linear equations and path problems, in Proc. 9th Annual Symposium on Theoretical Aspects of Computer Science (A. Finkel and M. Jantzen, eds.), Lecture Notes in Computer Science, Vol. 577, Springer-Verlag, Berlin, 1992, pp. 109-119.
28. M. Reid-Miller, G. L. Miller, and F. Modugno, List ranking and parallel tree contraction, in Synthesis of Parallel Algorithms (J. H. Reif, ed.), Morgan Kaufmann, San Mateo, CA, 1993, Chap. 3, pp. 115-194.
29. N. Robertson and P. D. Seymour, Graph Minors. II. Algorithmic aspects of tree-width, J. Algorithms, 7 (1986), 309-322.
30. B. Schieber and U. Vishkin, On finding lowest common ancestors: simplification and parallelization, SIAM J. Comput., 17 (1988), 1253-1262.
31. R. E. Steams and H. B. Hunt III, An algebraic model for combinatorial problems, SIAM J. Comput., 25 (1996), 448-476.
32. R. E. Tarjan and U. Vishkin, An efficient parallel biconnectivity algorithm, SIAM J. Comput., 14 (1985), 862-874.
33. J. van Leeuwen, Graph algorithms, in Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity (J. van Leeuwen, ed.), Elsevier, Amsterdam and The MIT Press, Cambridge, MA, 1990, Chap. 10, pp. 525-631.