• Corpus ID: 16891507

Efficient Algorithms for Network Optimization

  title={Efficient Algorithms for Network Optimization},
  author={Bobekt E. Taejae},
This paper is a survey of recent improvements in algorithms for four classical network optimization problems. The problems we consider are those of finding minimum spanning trees, shortest paths, maximum network flows, and maximum matchings. For each problem we summarize the history of work on the problem and the current state of the art. We conclude by discussing the techniques that have led to the most efficient known algorithms. 
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  • Mathematics
  • 2009
Steiner’s Problem is the ”Problem of shortest connectivity”, that means, given a finite set of points in a metric space X , search for a network interconnecting these points with minimal length. This


Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
New algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem are presented, and Dinic shows that, in a network with n nodes and p arcs, a maximum flow can be computed in 0 (n2p) primitive operations by an algorithm which augments along shortest augmenting paths.
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It is shown that $O(N^{5/2} )$ comparisons and additions suffice to solve the all-pairs shortest path problem for directed graphs on N vertices with nonnegative edge weights. In conjunction with
Efficient Algorithms for Shortest Paths in Sparse Networks
Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs, and a class of “arc set partition” algorithms is introduced.
Implementation and efficiency of Moore-algorithms for the shortest route problem
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  • Computer Science
    Math. Program.
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The main objective of this paper is to show the strong relationship between an algorithm and its implementation and to show a variant of Moore's method seems to be most efficient for different types of graph structures.
Flows in Networks
This chapter sees how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models” and finds an optimal solution that is integer-valued.
Shortest connection networks and some generalizations
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
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  • Computer Science
    Probability in the Engineering and Informational Sciences
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A modified version of the methods uses a coupling to give strong support to the design principle: It is better with few but quick servers.
Finding Minimum Spanning Trees
This paper studies methods for finding minimum spanning trees in graphs and results include relationships with other problems which might lead general lower bound for the complexity of the minimum spanning tree problem.
An O (N2.5) algorithm for maximum matching in general graphs
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  • Computer Science
    16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
  • 1975
This work presents a new efficient algorithm for finding a maximum matching in an arbitrary graph that is O(m√n¿log n) where n, m are the numbers of the vertices and the edges in the graph.
Scaling algorithms for network problems
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  • Computer Science
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
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This work presents efficient algorithms for network problems that work by scaling the numeric parameters, and gives simple algorithms that match the best time bounds for shortest paths on a directed graph with nonnegative lengths and maximum value network flow.