A polynomial time primal network simplex algorithm for minimum cost flows
- MIT, Cambridge, MA (United States)
In this extended abstract, we develop a polynomial time primal network simplex algorithm that runs in O(min(n{sup 2}m log nC, n{sup 2}m{sup 2} log n)) time, where n is the number of nodes in the network, in is the number of arcs, and C denotes the maximum absolute arc costs if arc costs are integer and {infinity} otherwise. We first introduce a pseudopolynomial variant of the network simplex algorithm called the {open_quotes}premultiplier algorithm.{close_quotes} A vector {pi} of node potentials is called a vector of premultipliers with respect to a rooted tree if each arc directed towards the root has a non-positive reduced cost and each arc directed away from the root has a non-negative reduced cost. We then develop a cost-scaling version of the premultiplier algorithm that solves the minimum cost flow problem in O(min(nm log nC, nm{sup 2} log n)) pivots. With certain simple data structures, the average time per pivot can be shown to be O(n).
- OSTI ID:
- 416832
- Report Number(s):
- CONF-960121--; CNN: Grant N00014-94-1-0099
- Country of Publication:
- United States
- Language:
- English
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