Scaling algorithms for network problems

Harold N. Gabow
1983 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)  
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
more » ... sults 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).
doi:10.1109/sfcs.1983.68 dblp:conf/focs/Gabow83 fatcat:tugysfkhs5apbi6bat6zsp6ieq