Abstract
Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G with the maximum number of edges. The algorithm that, given a connected graph G, outputs a spanning tree of G, is a \(\frac{1}{2}\)-approximation. Indeed, if n is the number of vertices in G, any spanning tree in G has n−1 edges and any series-parallel graph on n vertices has at most 2n−3 edges. We present a \(\frac{7}{12}\)-approximation for this problem and results showing the limits of our approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berman, P., Ramaiyer, V.: Improved approximations for the Steiner tree problem. J. Algorithms 17, 381–408 (1994)
Cai, L.: On spanning 2-trees in a graph. Discrete Appl. Math. 74(3), 203–216 (1997)
Cai, L., Maffray, F.: On the spanning k-tree problem. Discrete Appl. Math. 44, 139–156 (1993)
Călinescu, G., Fernandes, C.G., Finkler, U., Karloff, H.: A better approximation algorithm for finding planar subgraphs. J. Algorithms 27(2), 269–302 (1998)
Călinescu, G., Fernandes, C.G., Karloff, H., Zelikovski, A.: A new approximation algorithm for finding heavy planar subgraphs. Algorithmica 36(2), 179–205 (2003)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Robins, G., Zelikovsky, A.: Improved steiner tree approximation in graphs. In: Proceedings of the Tenth ACM-SIAM Symposium on Discrete Algorithms (SODA) pp. 770–779 (2000)
Schrijver, A.: Combinatorial Optimization, vol. A. Springer, Berlin (2003). Available at http://homepages.cwi.nl/lex/files/dict.ps
Tarjan, R.E.: Data Structures and Networks Algorithms. Society for Industrial and Applied Mathematics, Philadelphia (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version appeared in the proceedings of the 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009).
Research of G.C. was supported in part by NSF grants CCF-0515088 and NeTS-0916743, and performed in part while on sabbatical at University of Wisconsin Milwaukee.
Research of C.G.F. was supported in part by CNPq 312347/2006-5, 485671/2007-7, and 486124/2007-0.
Research of A.Z. was supported in part by NSF grant IIS-0916401 and NIFA award 2011-67016-30331.
Rights and permissions
About this article
Cite this article
Călinescu, G., Fernandes, C.G., Kaul, H. et al. Maximum Series-Parallel Subgraph. Algorithmica 63, 137–157 (2012). https://doi.org/10.1007/s00453-011-9523-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-011-9523-4