Some polyhedra related to combinatorial problems

Gröbner Basis Approach to Some Combinatorial Problems

We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the Gröbner basis of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.

Combinatorial problems related to origin-destination matrices

Some continuous functions related to corner polyhedra, II

The group problem on the unit interval is developed, with and without continuous variables. The connection with cutting planes, or valid inequalities, is reviewed. Certain desirable properties of valid inequalities, such as minimality and extremality are developed, and the connection between valid inequalities for P(I, u 0) and P+(I, u 0) is developed. A class of functions is shown to give extr...

Some combinatorial problems of importance

We discuss two combinatorial problems for which we have only sub-optimal solutions. We describe known solutions and we explain why better solutions would be of importance to Cryptography. The areas of application are in improving the ef-ciency of Zero-Knowledge proofs, in relating the quadratic residuosity problem to the problem of integer factorization, and in analyzing some cryptographic sche...

EDMONDS POLYHEDRA AND A HIERARCHY OF COMBINATORIAL PROBLEMS bY

Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality c aj xj 2 ao, where al, a2, . . . , an are integers, by the inequality c a. x < a with a 1 [a,]. Obviously, if J jintegers Xl' 5’ l *a 9 ⌧...