Let the elements of a matroid be labeled in an abelian group, and let \(F\) be a finite set of forbidden basis-label sums. We give an alternative proof of the sharp unweighted proximity bound established by Lizhong Chen: for every representable matroid, every basis is within \(|F|\) exchanges of an \(F\)-avoiding basis whenever one exists. … Read more
We study proximity (resp. integrality gap), that is, the distance (resp. difference) between the optimal solutions (resp. optimal values) of convex integer programs (IP) and the optimal solutions (resp. optimal values) of their continuous relaxations. We show that these values can be upper bounded in terms of the recession cone of the feasible region of … Read more
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2010, pp. 219–229], … Read more