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Minimum Spanning Trees

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Abstract

In this chapter, we study the behavior of stochastic search algorithms on an important graph problem. We consider the well-known problem of computing a minimum spanning tree in a given undirected connected graph with n vertices and m edges. The problem has many applications in the area of network design. Assume that we have n computers that should be connected with minimum cost, where costs of a certain amount occur when one computer is connected to another one. The cost for a connection can, for example, be the distance between two considered computers. One needs to make n−1 connections between these computers such that all computers are able to communicate with each other. Considering a graph as a model for a possible computer network, it has n vertices and one searches for the set of edges with minimal cost that makes the graph connected.

Keywords

  • Span Tree
  • Connected Graph
  • Minimum Span Tree
  • Search Point
  • Construction Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-16544-3_5
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Correspondence to Carsten Witt .

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© 2010 Springer-Verlag Berlin Heidelberg

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Neumann, F., Witt, C. (2010). Minimum Spanning Trees. In: Bioinspired Computation in Combinatorial Optimization. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16544-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-16544-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16543-6

  • Online ISBN: 978-3-642-16544-3

  • eBook Packages: Computer ScienceComputer Science (R0)