Abstract
An efficient approach, called deferred-query, is proposed in this paper to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit and matching problems on a set of sorted intervals. Using above results, the optimal path cover, hamiltonian path and hamiltonian circuit problems can also be solved in O(n) time on a set of sorted arcs.
Chapter PDF
Similar content being viewed by others
References
S. Rao Arikati and C. Pandu Rangan, Linear algorithm for optimal path cover problem on interval graphs, Inform. Process. Lett. 35 (1990), 149–153.
A. A. Bertossi, On the domatic number of interval graphs, Inform. Process. Lett. 28 (1988) 275–280.
A. A. Bertossi, The edge Hamiltonian path problem is NP-complete, Inform. Process. Lett. 13 (1981) 157–159.
A. A. Bertossi and M. A. Bonuccelli, Hamiltonian Circuits in Interval Graph Generalizations, Information Process. Lett. 23 (1986) 195–200.
M. A. Bonuccelli and D. P. Bovet, Minimum Node Disjoint Path Covering for Circular-Arc Graphs, Information Process. Lett. 8 (1979) 159–161.
K. S. Booth and G. S. Leuker, Testing for consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms, J. Comput. system Sci. 13 (1976), 335–379.
M. S Chang, O(n) Algorithms for the Hamiltonian Cycle and Node Disjoint Path Cover Problems on Circular-Arc Graphs, Preprint.
E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), 247–261.
M. S. Chang, S. L. Peng and J. L. Liaw, Deferred-Query, An Efficient Approach for Some Problems on Interval Graphs, Preprint.
M. Farber, Domination, independent domination, and duality in strongly chordal graphs, Disc. Appl. Math. 7 (1984), 115–130.
H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, J. Comput. System Sci. 30 (1985), 209–221.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, San Francisco, CA, 1979.
M. R. Garey, D. S. Johnson and R. E. Tarjan, The planar Hamiltonian circuit problem is NP-complete, SIAM J. Comput. 5 (1976), 704–714.
M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
M. C. Golumbic and P. L. Hammer, Stability in Circular-Arc Graphs, J. of Algorithms 9 (1988) 314–320.
W. L. Hsu, W. K. Shih and T. C. Chern, An O(n 2logn) Time Algorithm for the Hamiltonian Cycle Problem, SIAM J. on Compt.
W. L. Hsu and K. H. Tsai, Linear Time Algorithms on Circular-Arc Graphs, Information Process. Lett. 40 (1991) 123–129.
D. S. Johnson, The NP-Complete Column: an Ongoing Guide, J. of Algorithms 6 (1985) 434–451.
J. M. Keil, Finding Hamiltonian Circuits in Interval Graphs, Inform. Process. Lett. 20 (1985), 201–206.
M. S. Krishnamoorthy, An NP-hard problem in a bipartite graphs, SIGACT News 7 (1), (1976) 26.
T. L. Lu, P. H. Ho and G.J. Chang, The domatic number problem in interval graphs, SIAM J. Disc. Math. 3. (1990), 531–536.
G. K. Manacher and T. A. Mankus, Determining the domatic number and a domatic partition of an interval graph in time O(n) given its sorted model, Technique report, Submitted to SIAM J. Disc. Math. 1991.
G. K. Manacher, T. A. Mankus and C. J. Smith, An Optimum O(nlogn) Algorithm for Finding a Canonical Hamiltonian Path and a Canonical Hamiltonian circuit in a set of intervals, Inform. Process. Lett. 35 (1990), 205–211.
S. Masuda and K. Nakajima, An Optimal Algorithm for Finding a Maximum Independent Set of a Circular-Arc Graph, SIAM J. Comput. 17 (1988) 41–52.
A. Moitra and R. C. Johnson, A parallel algorithm for maximum matching on interval graphs, 1989 International Conference on Parallel Processing, III 114–120.
S. L. Peng and M. S. Chang, A new approach for domatic number problem on interval graphs, Proceedings of National Computer Symposium 1991 R.O.C., 236–241.
F. S. Roberts, Graph theory and its Applications to problems of society, SIAM, Philadelphia, PA, 1978.
A. Srinivasa Rao and C. Pandu Rangan, Linear algorithm for domatic number problem on interval graphs, Inform. Process. Lett. 33 (1989), 29–33.
A. Tucker, An Efficient Test for Circular-Arc Graphs, SIAM J. Comput. 9 (1980) 1–24.
P. Van Emde Boas, Preserving order in a forest in less than logarithmic time and linear space, Inform. Process. Lett. 6 (1977), 80–82.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chang, MS., Peng, SL., Liaw, JL. (1993). Deferred-query—An efficient approach for problems on interval and circular-arc graphs. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_250
Download citation
DOI: https://doi.org/10.1007/3-540-57155-8_250
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57155-1
Online ISBN: 978-3-540-47918-5
eBook Packages: Springer Book Archive