The Numerical Solution of Network Problems Using the Out-of-Kilter Algorithm

by R. J. Clasen

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An explanation of the Fulkerson network flow algorithm (P-1825) to provide practical guidance in applying it to computational problems. The Memorandum is divided into four substantially independent sections that (1) review the types of problems that can be represented as capacitated network problems; (2) explain (with diagrams) the out-of-kilter algorithm and techniques for implementing it on a computer; (3) describe modification to a two-phase algorithm; and (4) present a method for labeling the nodes by means of a scan list.It is tentatively concluded that the two-phase algorithm is undesirable and that the list structure procedure shortens computer time at the cost of using more memory. A 1530-arc problem on the IBM-360 Model 40 ran five times as fast using the list structures — 30 minutes, as compared with 2.5 hours for the searching technique.

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