Abstract
For many problems on permutation graphs, polynomial time bounds were found by using different approaches as e.g. dynamic programming, structural properties of the intersection model, the reformulation as a shortest-path problem on suitable derived graphs and a geometric representation as points in the plane. Here we outline these approaches and apply them to two problems: minimum weight independent dominating set and maximum weight cycle-free subgraph (minimum weight feedback vertex set).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
K. Arvind, C. Pandu Rangan: Connected domination and Steiner set on weighted permutation graphs, IPL 41 (1992), 215–220.
M.J. Atallah, S. Kosaraju: An Efficient Algorithm for Maxdominance with Applications, Algorithmica (1989) 4, 221–236.
M.J. Atallah, G.K. Manacher,J. Urrutia: Finding a minimum independent dominating set in a permutation graph, Discrete Applied Math., Vol 21, 177–183, 1988.
A. Brandstädt, D. Kratsch: On the restriction of some NP-complete graph problems to permutation graphs, L. Budach, ed., Proc. FCT 1985, Lecture Notes in Computer Science 199 (1985) 53–62, Fo.-erg. FSU Jena, N/84/80, 1984.
A. Brandstädt, D. Kratsch: On domination problems for permutation and other graphs, Theoretical Computer Science 54, 1987, 181–198.
C.J. Colbourn, L.K. Stewart: Permutation graphs: connected domination and Steiner trees, Topics on Domination, Annals of Discrete Mathematics 48 (Eds.: S.T. Hedetniemi, R.C. Laskar), 1990, 179–190.
D.G. Corneil, L.K. Stewart: Dominating sets in Perfect Graphs, Topics on Domination, Annals of Discrete Mathematics 48, 145–164.
S. Even, A. Pnueli, A. Lempel: Permutation graphs and transitive graphs, J. ACM, Vol 19, 400–410, 1972.
M. Farber, J.M. Keil: Domination in permutation graphs, J. Algorithms, Vol 6, 309–321, 1985.
V. Kamakoti, D. Kratsch, R. Mahesh, C. Pandu Rangan: A Unified Approach to Efficient Algorithms on weighted Permutation Graphs, manuscript 1991.
V. Kamakoti, C. Pandu Rangan: Efficient Transitive Reduction of Permutation graphs and its Applications, manuscript 1991.
H. Kim: Finding a maximum independent set in a permutation graph, Inf. Proc. Letters 36 (1990) 19–23.
E.L. Lawler: Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York 1976.
Y. Liang, C. Rhee, S.K. Dhall, S. Lakshmivarahan: A new approach for the domination problem on permutation graphs, Inf. Proc. Letters 37 (1991) 219–224.
G.K. Manacher, C.J. Smith, Efficient algorithms for new problems on interval graphs and interval models, manuscript, 1984.
A. Srinivasan, C. Pandu Rangan: Efficient algorithms for the minimum weighted dominating clique problem on permutation graphs, Theor. Comp. Sci. 91 (1991), 1–21.
A. Pnueli, A. Lempel, S. Even: Transitive orientation of graphs and identification of permutation graphs”, Canad.J. Math., Vol 23 (1971), 160–175.
J. Spinrad: On comparability and permutation graphs, SIAM J. Comput., Vol 14, 658–670, 1985.
J. Spinrad, A. Brandstädt, L. Stewart: Bipartite permutation graphs, Discrete Applied Math., Vol 18, 279–292, 1987.
K.H. Tsai, W.L. Hsu: Fast algorithms for the dominating set problem on permutation graphs, Internat. Sympos. SIGAL 1990, Lect. Notes in Comp. Sci. 450, 109–117.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brandstädt, A. (1993). On improved time bounds for permutation graph problems. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_30
Download citation
DOI: https://doi.org/10.1007/3-540-56402-0_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56402-7
Online ISBN: 978-3-540-47554-5
eBook Packages: Springer Book Archive