Abstract
We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, “difficult” inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cycle can be discarded. Previously this has only been exploited in asymptotically optimal algorithms that are considered impractical. An additional advantage is that the algorithm can greatly profit from pipelined memory access. Hence, an implementation on a vector machine is up to 10 times faster than previous algorithms. We outline additional refinements for MSTs of implicitly defined graphs and the use of the central data structure for querying the heaviest edge between two nodes in the MST. The latter result is also interesting for sparse graphs.
Partially supported by DFG grant SA 933/1-1.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alon, N., Schieber, B.: Optimal preprocessing for answering on-line product queries. Technical Report TR 71/87, Tel Aviv University (1987)
Boruvka, O.: O jistém problému minimálním. Pràce, Moravské Prirodovedecké Spolecnosti, pp. 1–58 (1926)
Fredman, M.L.: On the efficiency of pairing heaps and related data structures. Journal of the ACM 46(4), 473–501 (1999)
Jájá, J.: An Introduction to Parallel Algorithms. Addison-Wesley, Reading (1992)
Jarník, V.: O jistém problému minimálním. Práca Moravské Pr̆írodovĕdecké Spolec̆nosti 6, 57–63 (1930)
Karger, D., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm for finding minimum spanning trees. Journal of the ACM 42(2), 321–329 (1995)
King, V.: A simpler minimum spanning tree verification algorithm. Algorithmica 18, 263–270 (1997)
Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm for finding minimum spanning trees. In: Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, pp. 9–15 (1994)
Komlós, J.: Linear verification for spanning trees. In: 25th annual Symposium on Foundations of Computer Science, pp. 201–206 (1984)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society 7, 48–50 (1956)
Mehlhorn, K., Näher, S.: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)
Moret, B.M.E., Shapiro, H.D.: An empirical analysis of algorithms for constructing a minimum spanning tree. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1991. LNCS, vol. 519, pp. 400–411. Springer, Heidelberg (1991)
Nesetril, J., Milková, E., Nesetrilová, H.: Otakar Boruvka on minimum spanning tree problem: Translation of both the 1926 papers, comments, history. Discrete Mathematics 233(1-3), 3–36 (2001)
Pettie, S., Ramachandran, V.: An optimal minimum spanning tree algorithm. Journal of the ACM 49(1), 16–34 (2002)
Prim, R.C.: Shortest connection networks and some generalizations. Bell Systems Technical Journal, 1389–1401 (1957)
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
Katriel, I., Sanders, P., Träff, J.L. (2003). A Practical Minimum Spanning Tree Algorithm Using the Cycle Property. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_61
Download citation
DOI: https://doi.org/10.1007/978-3-540-39658-1_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20064-2
Online ISBN: 978-3-540-39658-1
eBook Packages: Springer Book Archive