Gomory: cutting away a fractional answer without losing integer solutions

What changed

Scientific scope

A mechanical fractional-tableau cut that preserves integer feasibility while excluding the fractional incumbent; a finite integer algorithm is announced, with its complete termination argument deferred. Exact 1958 Bulletin AMS 64(5), 275-278 announcement; Damaged tableau notation and computer-model text are not certified transcriptions. The displayed construction uses nonnegative integer variables, including objective and slack variables; modern mixed-integer cuts are a different target. Page 276 and page 278 explicitly defer the complete termination-enforcing choices and finiteness proof to a longer paper. The supplied cut-validity explanation does not make arbitrary row-selection heuristics convergent. Earlier manually constructed cuts by Dantzig/Fulkerson/Johnson and Markowitz/Manne are acknowledged. The largest reported small test had at most seven variables; no modern solver benchmark or general efficiency claim is established. Row selection is nonunique and the suggested deepest-fraction rule is heuristic. A. Tucker communicated the note and Princeton-IBM supplied institutional support; neither role is coauthorship. Later complete algorithms, mixed-integer variants and branch-and-cut implementations remain separate.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Ralph E. Gomory · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

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