Set covering polyhedra graphs, and matroids

我的主要兴趣领域是组合优化，特别是称为打包和覆盖的整数规划模型。各种各样的实际问题可以在这种设置中形成，包括：调度问题，分配问题，以及通过网络运输一种或多种商品的问题。有时，由于问题的特殊结构，自然线性规划松弛产生最优解。当这种情况发生时，问题就可以有效地解决。我研究的重点是描述这种现象发生的时间。尽管这些模型植根于现实生活，但这导致了纯粹数学性质的深刻问题。

My primary area of interest is combinatorial optimization, in particular the integer programming models known as packing and covering. A wide variety of practical questions can be formulated in this setting and include: scheduling problems, assignment problems, and the problem of shipping one or more commodities across a network. Sometimes, owing to the special structure of the problem, the natural linear programming relaxation yields an optimal solution. When this occurs the problem can be solved efficiently. The focus of my research has been to characterize when this phenomenon occurs. Although these models have their roots in real life, this leads to deep questions of a purely mathematical nature.