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Randomized Minimum Spanning Tree

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 163 Accesses

Years and Authors of Summarized Original Work

  • 1995; Karger, Klein, Tarjan

Problem Definition

The input to the problem is a connected undirected graph G = (V, E) with a weight w(e) on each edge e ∈ E. The goal is to find a spanning tree of minimum weight, where for any subset of edges \(E^{{\prime}}\subseteq E\), the weight of\(E^{{\prime}}\) is defined to be \(w(E^{{\prime}}) =\sum \limits _{e\in E^{{\prime}}}w(e)\).

If the graph G is not connected, the goal of the problem is to find a minimum spanning forest, which is defined to be a minimum spanning tree in each connected component of G. Both problems will be referred to as the MST problem.

The randomized MST algorithm by Karger, Klein, and Tarjan [9] which is considered here will be called the KKT algorithm. Also it will be assumed that the input graph G = (V, E) has n vertices and m edges and that the edge weights are distinct.

The MST problem has been studied extensively prior to the KKT result, and several very efficient,...

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Acknowledgements

This work was supported in part by NSF grant CFF-0514876.

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Authors and Affiliations

  1. Computer Science, University of Texas, Taylor Hall 2.124 (Mailcode C0500), 78712-1188, Austin, TX, USA

    Vijaya Ramachandran

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  1. Vijaya Ramachandran
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Correspondence to Vijaya Ramachandran .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Ramachandran, V. (2016). Randomized Minimum Spanning Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_325

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