Abstract
The weighted m -d matching and m -set packing problems (m ≥ 3) are usually solved through approximation algorithms. In this paper, we define the parameterized versions of these problems and study their algorithms. For the weighted m -set packing problem, we develop a parameterized algorithm of running time O(12.8mk n O(1)), which is based on the recently improved color-coding technology and dynamic programming. By refining the techniques, we also develop a more efficient parameterized algorithm of running time O(12.8(m − 1)k n O(1)) for the weighted m -d matching problem, which is a restricted version of the weighted m -set packing problem.
This work is supported by the National Natural Science Foundation of China (60433020) and the Program for New Century Excellent Talents in University (NCET-05-0683).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Yuster, R., Zwick, U.: Color-coding. Journal of the ACM 42, 844–856 (1995)
Chandra, B., Halldorsson, M.: Greedy local improvement and weighted set packing approximation. Journal of Algorithms 39, 223–240 (2001)
Chen, J., et al.: Improved algorithms for path, matching, and packing problems. In: Proc. 18th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 07), pp. 298–307 (2007)
Fellows, M., et al.: Finding k disjoint triangles in an arbitrary graph. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 235–244. Springer, Heidelberg (2004)
Fellows, M.R., et al.: Faster Fixed-parameter tractable algorithms for matching and packing problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 311–322. Springer, Heidelberg (2004)
Fernau, H.: Parameterized maximization. Technical Report WSI-2001-22, UniversityTubingen (Germany), Wilhelm-Schickard-Institut fur Informatik (2001)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Guo, J., Niedermeier, R.: Exact algorithms and applications for tree-like weighted set cover. Journal of Discrete Algorithms 4, 608–622 (2006)
Jia, W., Zhang, C., Chen, J.: An efficient parameterized algorithm for m-Set Packing. Journal of Algorithms 50, 106–117 (2004)
Liu, Y., et al.: Greedy localization and color-coding: improved matching and packing algorithms. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 84–95. Springer, Heidelberg (2006)
Mathieson, L., Prieto, E., Shaw, P.: Packing edge disjoint triangles: a parameterized view. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 127–137. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, Y., Chen, J., Wang, J. (2007). Parameterized Algorithms for Weighted Matching and Packing Problems. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_63
Download citation
DOI: https://doi.org/10.1007/978-3-540-72504-6_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72503-9
Online ISBN: 978-3-540-72504-6
eBook Packages: Computer ScienceComputer Science (R0)