Integer Minkowski Programs and the Design of Survivable Networks

Eisenschmidt, Elke; Köppe, Matthias; Laugier, Alexandre

Integer Minkowski Programs and the Design of Survivable Networks

Authors

Eisenschmidt, Elke

Köppe, Matthias

Laugier, Alexandre

Description

We introduce a new class of optimization problems called integer Minkowski programs. The formulation of such problems involves finitely many integer variables and nonlinear constraints involving functionals defined on families of discrete or polyhedral sets. We show that, under certain assumptions, it is possible to reformulate them as integer linear programs, by making use of integral generating sets. We then apply this technique to the network design problem for fractional and integral flows subject to survivability constraints.
27 pages, 9 figures