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Finding the Optimum

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Abstract

A country with n towns wants to construct a new telephone network to connect all towns. Of course, they don’t have to build a separate line between every pair of towns; but they do need to build a connected network; in our terms, this means that the graph of direct connections must form a connected graph. Let’s assume that they don’t want to build a direct line between towns that can be reached otherwise (there may be good reasons for doing so, as we shall see later, but at the moment let’s assume their only goal is to get a connected network). Thus they want to build a minimal connected graph with these nodes, i.e., a tree.

Keywords

  • Span Tree
  • Connected Graph
  • Triangle Inequality
  • Connected Network
  • Travel Salesman Problem

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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Lovász, L., Pelikán, J., Vesztergombi, K. (2003). Finding the Optimum. In: Discrete Mathematics. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/0-387-21777-0_9

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  • DOI: https://doi.org/10.1007/0-387-21777-0_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-95585-8

  • Online ISBN: 978-0-387-21777-2

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