Online promise problems with online width metrics

Journal of Computer and System Sciences

Volumn 73, Issue 1, 2007, Pages 57-72

  Downey, Rodney G ^a   McCartin, Catherine ^b  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^b MASSEY UNIVERSITY   (New Zealand)

Author keywords

Online algorithms; Online coloring; Parameterized complexity; Pathwidth; Persistence; Treewidth

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY;

ONLINE ALGORITHMS; ONLINE COLORING; PARAMETERIZED COMPLEXITY; PATHWIDTH; PERSISTENCE; TREEWIDTH;

PROBLEM SOLVING;

EID: 33750974765     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2006.08.002     Document Type: Article

References (30)

1. Arnborg S., Corneil D.G., and Proskurowski A. Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth. 8 (1987) 277-284
2. Bodlaender H.L. A linear time algorithm for finding tree decompositions of small treewidth. SIAM J. Comput. 25 (1996) 1305-1317
3. H.L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Technical Report UU-CS-1996-02, Department of Computer Science, Utrecht University, Utrecht, 1996
4. Bodlaender H.L. Treewidth: Algorithmic techniques and results. Proc. 22nd MFCS. Lecture Notes in Comput. Sci. vol. 1295 (1997), Springer-Verlag 19-36
5. Bodlaender H.L., and Engelfreit J. Domino treewidth. J. Algorithms 24 (1997) 94-127
6. Bodlaender H.L., Fellows M.R., and Hallett M.T. Beyond NP-completeness for problems of bounded width: Hardness for the W-hierarchy. Proc. 26th Annual Symposium on Theory of Computing (1994), ACM Press, New York 449-458
7. Bodlaender H.L., and Kloks T. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms 21 (1996) 358-402
8. Chrobak M., and Slusarek M. On some packing problems related to dynamic storage allocation. RAIRO Inform. Theor. Appl. 22 (1988) 487-499
9. Downey R.G., and Fellows M.R. Parameterized Complexity (1999), Springer-Verlag
10. Fellows M.R., and Langston M.A. An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations. Proceedings of the 30th Annual Symposium on Foundations of Computer Science (1989), IEEE Computer Science Press, Los Alamitos, CA 520-525
11. B. de Fluiter, Algorithms for graphs of small treewidth, PhD thesis, University of Utrecht, Utrecht, 1997
12. J. Fouhy, Computational experiments on graph width metrics, MSc thesis, Victoria University, Wellington, 2003
13. Gyarfas A., and Lehel J. On-line and first fit coloring of graphs. J. Graph Theory 12 2 (1988) 217-227
14. Lagergren J. Efficient parallel algorithms for graphs of bounded treewidth. J. Algorithms 20 (1996) 20-44
15. Irani S. Coloring inductive graphs on-line. Algorithmica 11 (1994) 53-72
16. Kierstead H.A. Recursive and on-line graph coloring. Handbook of Recursive Mathematics, vol. 2 (1998), Elsevier 1233-1269
17. Kierstead H.A. The linearity of first fit coloring of interval graphs. SIAM J. Discrete Math. 1 4 (1988) 526-530
18. Kierstead H.A., and Qin J. Coloring interval graphs with first-fit. In: Aigner M., and Wille R. (Eds). Special Issue: Combinatorics of Ordered Sets, papers from the 4th Oberwolfach Conf. 1991. Discrete Math. 144 (1995) 47-57
19. Kierstead H.A., and Trotter W.A. An extremal problem in recursive combinatorics. Congr. Numer. 33 (1981) 143-153
20. Kirousis L.M., and Thilikos D.M. The linkage of a graph. SIAM J. Comput. 25 3 (1996) 626-647
21. Lovasz L., Saks M.E., and Trotter W.A. An on-line graph coloring algorithm with sublinear performance ratio. Discrete Math. 75 (1989) 319-325
22. Manasse M.S., McGeoch L.A., and Sleator D.D. Competitive algorithms for online problems. Proceedings of the 20th Annual ACM Symposium on Theory of Computing. Chicago (1988), ACM Press, New York 322-333
23. Matousek J., and Thomas R. Algorithms for finding tree-decompositions of graphs. J. Algorithms 12 (1991) 1-22 in: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, 1988, pp. 322-333
24. C.M. McCartin, Contributions to parameterized complexity, PhD thesis, Victoria University, Wellington, 2003
25. Perkovic L., and Reed B. An improved algorithm for finding tree decompositions of small width. Internat. J. Found. Comput. Sci. 11 3 (2000) 365-371
26. Reed B. Finding approximate separators and computing treewidth quickly. Proceedings of the 24th Annual Symposium on Theory of Computing (1992), ACM Press, New York 221-228
27. Robertson N., and Seymour P.D. Graph minors-A Survey. In: Anderson I. (Ed). Surveys in Combinatorics (1985), Cambridge Univ. Press 153-171
28. Robertson N., and Seymour P.D. Graph minors II. Algorithmic aspects of tree-width. J. Algorithms 7 (1986) 309-322
29. Sleator D.D., and Tarjan R.E. Amortized efficiency of list update and paging rules. Com. ACM 28 (1985) 202-208
30. M. Szegedy, private communication, reported in [16]