Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T03:29:04.510Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimum convex-cost tension problemson series-parallel graphs

Published online by Cambridge University Press:  15 March 2004

Bruno Bachelet  and
Philippe Mahey
Bruno Bachelet
Affiliation:
LIMOS, UMR 6158-CNRS, Université Blaise-Pascal, BP 10125, 63173 Aubière, France; [email protected]., [email protected].
Philippe Mahey
Affiliation:
LIMOS, UMR 6158-CNRS, Université Blaise-Pascal, BP 10125, 63173 Aubière, France; [email protected]., [email protected].
Get access

Abstract

We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O(m3) operations.

Keywords

Minimum cost tensionconvex piecewise linear costsseries-parallel graphs.
Type
Research Article
Information
RAIRO - Operations Research , Volume 37 , Issue 4: ROADEF 2002 , October 2003 , pp. 221 - 234
Copyright
© EDP Sciences, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahuja, R.K., Hochbaum, D.S. and Orlin, J.B., Solving the Convex Cost Integer Dual Network Flow Problem. Lect. Notes Comput. Sci. 1610 (1999) 31-44. CrossRef
R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows - Theory, Algorithms, and Applications. Prentice Hall (1993).
Allen, J.F., Maintaining Knowledge about Temporal Intervals. Commun. ACM 26 (1983) 832-843 . CrossRef
B. Bachelet, B++ Library. http://frog.isima.fr/bruno/?doc=bpp_library
Bachelet, B. and Mahey, P., Optimisation de la présentation d'un document hypermédia. Ann. Sci. Univ. Blaise Pascal 110 (2001) 81-90.
B. Bachelet, P. Mahey, R. Rodrigues and L.F. Soares, Elastic Time Computation for Hypermedia Documents. SBMidìa (2000) 47-62 .
C. Berge and A. Ghoula-Houri, Programmes, jeux et réseaux de transport. Dunod (1962).
Bern, M.W., Lawler, E.L. and Wong, A.L., Linear-Time Computation of Optimal Subgraphs of Decomposable Graphs. J. Algorithms 8 (1987) 216-235 . CrossRef
M.C. Buchanan and P.T. Zellweger, Specifying Temporal Behavior in Hypermedia Documents. Eur. Conference on Hypertext '92 (1992) 262-271.
M.C. Buchanan and P.T. Zellweger, Automatically Generating Consistent Schedules for Multimedia Documents. Multimedia Systems (1993) 55-67.
Datta, A.K. and Sen, R.K., Efficient Scheme, An to Solve Two Problems for Two-Terminal Series Parallel Graphs. Inform. Proc. Lett. 71 (1999) 9-15 . CrossRef
Duffin, R.J., Topology of Series-Parallel Networks. J. Math. Anal. Appl. 10 (1965) 303-318 . CrossRef
Eppstein, D., Parallel Recognition of Series-Parallel Graphs. Inform. Comput. 98 (1992) 41-55 . CrossRef
Fulkerson, D.R., Out-of-Kilter Method, An for Minimal Cost Flow Problems. SIAM J. Appl. Math. 9 (1961) 18-27. CrossRef
Hadjiat, M., Penelope's Graph: a Hard Minimum Cost Tension Instance. Theoret. Comput. Sci. 194 (1998) 207-218 . CrossRef
Ho, C.W., Hsieh, S.Y. and Chen, G.H., Parallel Decomposition of Generalized Series-Parallel Graphs. J. Inform. Sci. Engineer. 15 (1999) 407-417.
M.Y. Kim and J. Song, Multimedia Documents with Elastic Time. Multimedia '95 (1995) 143-154.
An Out-of-Kilter Al, J.M. Plagorithm for Solving Minimum Cost Potential Problems. Math. Programming 1 (1971) 275-290 .
R.T. Rockefellar, Convex Analysis. Princeton University Press (1970).
B. Schoenmakers, A New Algorithm for the Recognition of Series Parallel Graphs. Technical report, No CS-59504, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands (1995).
Takamizawa, K., Nishizeki, T. and Saito, N., Linear-Time Computability of Combinatorial Problems on Series-Parallel Graphs. J. ACM 29 (1982) 623-641 . CrossRef
Valdes, J., Tarjan, R.E. and Lawler, E.L., The Recognition of Series Parallel Digraphs. SIAM J. Comput. 11 (1982) 298-313 . CrossRef