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Abstract

We present a randomized parallel algorithm to find a minimum spanning forest (MSF) in a weighted, undirected graph. On an EREW PRAM our algorithm runs in logarithmic time and linear work w.h.p. This is both time and work optimal and is the first provably optimal parallel algorithm under both measures.

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References

  1. [AS87]
    Awerbuch, B., Shiloach, Y.: New connectivity and MSF algorithms for shuffle-exchange networks and PRAM. IEEE Trans. Computers C-36, 1258–1263 (1987)Google Scholar
  2. [Bor26]
    Borůvka, O.: O jistém problému minimaélním. Moravské Přírodovédecké Společnosti 3, 37–58 (1926) ( in Czech)Google Scholar
  3. [CHL99]
    Chong, K.W., Han, Y., Lam, T.W.: On the parallel time complexity of undirected connectivity and minimum spanning trees. In: Proc. SODA 1999, pp. 225–234 (1999)Google Scholar
  4. [CKT94]
    Cole, R., Klein, P.N., Tarjan, R.E.: A linear-work parallel algorithm for finding minimum spanning trees. In: Proc. SPAA, pp. 11–15 (1994)Google Scholar
  5. [CKT96]
    Cole, R., Klein, P.N., Tarjan, R.E.: Finding minimum spanning trees in logarithmic time and linear work using random sampling. In: Proc. SPAA, pp. 213–219 (1996)Google Scholar
  6. [Gaz91]
    Gazit, H.: An optimal randomized parallel algorithm for finding connected components in a graph. In: SICOMP, vol. 20, pp. 1046–1067 (1991)Google Scholar
  7. [GMR94]
    Gibbons, P.B., Matias, Y., Ramachandran, V.: The QRQW PRAM: Accounting for contention in parallel algorithms. In: Proc. SODA, pp. 638–648 (1994) (SICOMP 1999, to appear)Google Scholar
  8. [GMR97]
    Gibbons, P.B., Matias, Y., Ramachandran, V.: Can a shared-memory model serve as a bridging model for parallel computation? In: Proc. SPAA, pp. 72–83 (1997); Theory of Comp. Sys. (1999) (to appear)Google Scholar
  9. [HZ94]
    Halperin, S., Zwick, U.: An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM. In: Proc. SPAA, pp. 1–10 (1994)Google Scholar
  10. [HZ96]
    Halperin, S., Zwick, U.: Optimal randomized EREW PRAM algorithms for rinding spanning forests and for other basic graph connectivity problems. In: Proc. SODA 1996, pp. 438–447 (1996)Google Scholar
  11. [JM92]
    Johnson, D.B., Metaxas, P.: Connected components in O(log3/2 n) parallel time for CREW PRAM. JCSS 54, 227–242 (1997)zbMATHMathSciNetGoogle Scholar
  12. [King97]
    King, V.: A simpler minimum spanning tree verification algorithm. Algorithmica 18, 263–270 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  13. [KKT95]
    Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm to find minimum spanning trees. JACM 42, 321–328 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  14. [KPRS97]
    King, V., Poon, C.K., Ramachandran, V., Sinha, S.: An optimal EREW PRAM algorithm for minimum spanning tree verification. IPL 62(3), 153–159 (1997)CrossRefMathSciNetGoogle Scholar
  15. [PR97]
    Poon, C.K., Ramachandran, V.: A randomized linear work EREW PRAM algorithm to find a minimum spanning forest. In: Leong, H.-V., Jain, S., Imai, H. (eds.) ISAAC 1997. LNCS, vol. 1350, pp. 212–222. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. [PR98]
    Poon, C.K., Ramachandran, V.: Private communication (1998)Google Scholar
  17. [PR99]
    Pettie, S., Ramachandran, V.: A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest Tech. Report TR99-13, Univ. of Texas at Austin (1999) Google Scholar
  18. [Val90]
    Valiant, L.G.: A bridging model for parallel computation. CACM 33(8), 103–111 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Seth Pettie
    • 1
  • Vijaya Ramachandran
    • 1
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustinUSA

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