## Scaling Algorithms for Network Problems (1985)

Citations: | 60 - 2 self |

### BibTeX

@MISC{Gabow85scalingalgorithms,

author = {Harold N. Gabow},

title = { Scaling Algorithms for Network Problems},

year = {1985}

}

### OpenURL

### Abstract

This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3 % log N) time. For appropriate N this improves the traditional Hungarian method, whose most efftcient implementation is O(n(m + n log n)). The speedup results from finding augmenting paths in batches. The matching algorithm gives similar improvements for the following problems: single-source shortest paths for arbitrary edge lengths (Bellman’s algorithm); maximum weight degree-constrained subgraph; minimum cost flow on a cl network. Scaling gives a simple maximum value flow algorithm that matches the best known bound (Sleator and Tarjan’s algorithm) when log N = O(log n). Scaling also gives a good algorithm for shortest paths on a directed graph with nonnegative edge lengths (Dijkstra’s algorithm).