A simple proof of finiteness is given for the simplex method under an easily described pivoting rule. A second new finite version of the simplex method is also presented.

It is shown that a binary matroid is orientable if and only if it is unimodular (regular), and that every unimodULAR matroid has an orientation that is induced by a coordinatization and is unique in a certain straightforward sense.Expand

Issues have in general not been well understood, including the exact character of the ellipsoid method and of Khachiyan''s result on polynomiality, its practical significance inlinear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work.Expand

A pivoting operation for oriented matroids and a finite pivoting method, which elucidate the combinatorial nature of Dantzig's simplex method, are described.Expand

Determining efficient sequences of X-ray diffraction measurements on a four-circle diffractometer leads to extremely large traveling salesman problems. Simple TSP heuristics give substantial… Expand

Issues have, in general, not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance inlinear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work.Expand

Padberg's conditions are sufficiently restrictive to suggest the possibility of establishing the Strong Perfect Graph Conjecture by proving that any graph G satisfying these conditions must contain a spanning subgraph isomorphic to C"@a"@w"+"1^@w, [email protected](G) = @w.Expand

A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined, and median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated.Expand