Abstract
Graph partitioning is an important subproblem in many applications. To solve it efficiently, the multilevel strategy in combination with a matching algorithm and a local refinement heuristic has proven to be a powerful method, and several libraries exist providing such an implementation. Due to the large involvement of heuristics, the evaluation of these libraries is usually based on experiments. In this paper we show that single experiments are usually not sufficient to judge the quality of an algorithm, since even results obtained for graphs of and identical structure show high variations. This is still true, even if the applied algorithms do not contain any nondeterminism. We propose a scheme that considers these variations and therefore makes evaluations and comparisons of different implementations more meaningful. We have applied this technique to evaluate the improvements of the Helpful-Set 2-partitioning implementation and present the obtained results.
This work was partly supported-by the German Science Foundation (DFG) project SFB-376.
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
R. Diekmann, B. Monien, and R. Preis. Using helpful sets to improve graph bisections. In D.F. Hsu, A.L. Rosenberg, and D. Sotteau, editors, Interconnection Networks and Mapping and Scheduling Parallel Computations, volume 21 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 57–73. AMS, 1995.
U. Elsner. Static and Dynamic Graph Partitioning. PhD thesis, Technische Universität Chemniz, 2001.
C. M. Fiduccia and R. M. Mattheyses. A linear-time heuristic for improving network partitions. In ACM IEEE Nineteenth Design Automation Conference Proceedings, pages 175–181, Los Alamitos, Ca., USA, Jun 1982. IEEE Computer Society Press.
B. Hendrickson and R. Leland. A multi-level algorithm for partitioning graphs. In Proceedings of Supercomputing’95, San Diego, CA, Dec 1995. ACM/IEEE.
J. Hromkovic and B. Monien. The bisection problem for graphs of degree 4 (configuring transputer systems). In A. Tarlecki, editor, Proceedings of Mathematical Foundations of Computer Science. (MFCS’ 91), volume 520 of LNCS, pages 211–220, Berlin, Germany, Sep 1991. Springer.
G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359–392, Jan 1999.
B. W. Kernighan and S. Lin. An efficient heuristic for partitioning graphs. Bell Systems Technical Journal, 49:291–308, Feb 1970.
C. Walshaw and M. Cross. Mesh partitioning: A multilevel balancing and refinement algorithm. SIAM Journal on Scientific Computing, 22(1):63–80, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schamberger, S. (2003). Improvements to the Helpful-Set Algorithm and a New Evaluation Scheme for Graph-Partitioners. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_6
Download citation
DOI: https://doi.org/10.1007/3-540-44842-X_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40156-8
Online ISBN: 978-3-540-44842-6
eBook Packages: Springer Book Archive