Shortest connection networks and some generalizations

  title={Shortest connection networks and some generalizations},
  author={Robert C. Prim},
  journal={Bell System Technical Journal},
  • R. Prim
  • Published 1 November 1957
  • Mathematics
  • Bell System Technical Journal
The basic problem considered is that of interconnecting a given set of terminals with a shortest possible network of direct links. Simple and practical procedures are given for solving this problem both graphically and computationally. It develops that these procedures also provide solutions for a much broader class of problems, containing other examples of practical interest. 
Some experiments with Steiner trees
The first results of investigation of this problem with the costs of the network nonlinearly dependent of the structure of thenetwork are shown.
Topological considerations in the design of optimum teleprocessing tree networks
A graph-theoretic approach to the design of optimum communication networks is given. The solution obtained satisfies the minimum cost weight, and is feasible and reliable. The paper also presents a
Some problems in discrete optimization
  • T. C. Hu
  • Computer Science
    Math. Program.
  • 1971
The present paper concentrates on several problems of network flows and discrete optimization, some of which are shortest paths, multi-commodity flows, traveling salesman problems, m-center problem, telepak problems and binary trees.
Network Design Techniques
In this chapter, a number of fundamental network design issues are considered and some potential techniques for solving them are presented and some basic subproblems associated with data communications network design are established.
Complexity of Optimum Undirected Tree Problems: A Survey of Recent Results
This work summarizes some recent results about the computational complexity of these problems with the aim of identifying the borderline between “easy” and “hard” problems.
Network decomposition for the optimization of connection structures
New decomposition methods for the determination of optimal paths without interference (independent decom position), of k node-disjoint paths with minimal total costs and of optimal Steiner trees are presented.
Efficient Algorithms for Network Optimization
This paper is a survey of recent improvements in algorithms for four classical network optimization problems, those of finding minimum spanning trees, shortest paths, maximum network flows, and maximum matchings.
Topological network synthesis
Several families of deterministic network optimization problems of particular importance for the design (synthesis) of real-life transportation, communication, and distribution networks are considered, including determination of optimal spanning and Steiner trees, multiconnected networks, distance bounded networks.


On the shortest spanning subtree of a graph and the traveling salesman problem
7. A. Kurosh, Ringtheoretische Probleme die mit dem Burnsideschen Problem uber periodische Gruppen in Zussammenhang stehen, Bull. Acad. Sei. URSS, Ser. Math. vol. 5 (1941) pp. 233-240. 8. J.