Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Distributed Algorithms for Minimum Spanning Trees

1983; Gallager, Humblet, Spira
  • Sergio Rajsbaum
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_116

Keywords and Synonyms

Minimum weight spanning tree      

Problem Definition

Consider a communication network, modeled by an undirected weighted graph \( { G = (V,E) } \)

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Recommended Reading

  1. 1.
    Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election and related problems (detailed summary). In: Proc. of the 19th Annual ACM Symposium on Theory of Computing, pp. 230–240. ACM, USA (1987)Google Scholar
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    Borůvka, O.: Otakar Borůvka on minimum spanning tree problem (translation of both the 1926 papers, comments, history). Disc. Math. 233, 3–36 (2001)CrossRefGoogle Scholar
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    Burns, J.E.: A formal model for message-passing systems. Indiana University, Bloomington, TR-91, USA (1980)Google Scholar
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    Frederickson, G., Lynch, N.: The impact of synchronous communication on the problem of electing a leader in a ring. In: Proc. of the 16th Annual ACM Symposium on Theory of Computing, pp. 493–503. ACM, USA (1984)Google Scholar
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    Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Prog. Lang. Systems 5(1), 66–77 (1983)zbMATHCrossRefGoogle Scholar
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    Johansen, K.E., Jorgensen, U.L., Nielsen, S.H.: A distributed spanning tree algorithm. In: Proc. 2nd Int. Workshop on Distributed Algorithms (DISC). Lecture Notes in Computer Science, vol. 312, pp. 1–12. Springer, Berlin Heidelberg (1987)Google Scholar
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    Korach, E., Moran, S., Zaks, S.: Tight upper and lower bounds for some distributed algorithms for a complete network of processors. In: Proc. 3rd Symp. on Principles of Distributed Computing (PODC), pp. 199–207. ACM, USA (1984)CrossRefGoogle Scholar
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    Korach, E., Moran, S., Zaks, S.: The optimality of distributive constructions of minimum weight and degree restricted spanning trees in a complete network of processors. In: Proc. 4th Symp. on Principles of Distributed Computing (PODC), pp. 277–286. ACM, USA (1985)Google Scholar
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    Lotker, Z., Patt-Shamir, B., Pavlov, E., Peleg, D.: Minimum-weight spanning tree construction in \( { O(\log\log n) } \) communication rounds. SIAM J. Comput. 35(1), 120–131 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
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    Lotker, Z., Patt-Shamir, B., Peleg, D.: Distributed MST for constant diameter graphs. Distrib. Comput. 18(6), 453–460 (2006)CrossRefGoogle Scholar
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    Moses, Y., Shimony, B.: A new proof of the GHS minimum spanning tree algorithm. In: Distributed Computing, 20th Int. Symp. (DISC), Stockholm, Sweden, September 18–20, 2006. Lecture Notes in Computer Science, vol. 4167, pp. 120–135. Springer, Berlin Heidelberg (2006)Google Scholar
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    Wu, B.Y., Chao, K.M.: Spanning Trees and Optimization Problems (Discrete Mathematics and Its Applications). Chapman Hall, USA (2004)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Sergio Rajsbaum
    • 1
  1. 1.Math InstituteNational Autonomous University of MexicoMexico CityMexico