NSF/CBMS Regional Conference in the Mathematical Sciences "Combinatorial Optimization:Packing and Covering" 5/18/99- 5/22/99

组合优化涉及从大量隐式描述的集合中有效地选择最优元素。这类问题的实例出现在许多重要的应用领域(例如，航空公司机组人员调度、制造物流、VLSI-电路设计、路线选择和实验设计)。许多这样的问题可以表示为整数规划的打包或覆盖问题。事实上，这样的提法一直是解决其中许多问题的最成功的手段。有用的算法和结构见解通常直接影响我们解决这些问题的实际实例的能力，这些见解是通过整数多面体、图、超图、拟阵和杂波的理论实现的。特别是，分解方法发挥着核心作用。我们的项目是一个为期五天的会议，在肯塔基大学举行，致力于这个主题。这次会议的主要活动是卡内基梅隆大学的Gerard Cornuejols博士的十个系列讲座。这些讲座将有助于向数学家(离散数学和其他领域的知名研究人员、博士后研究员和研究生)介绍包装和覆盖方面的当前研究。这次会议特别及时，因为在过去的几年里，该领域在理论和应用方面都有了快速的发展。

Combinatorial optimization involves the efficient choice of an optimal element from a large, implicitly-described set. Instances of such problems occur in many important applied domains (e.g., airline-crew scheduling, manufacturing logistics, VLSI-circuit design, routing, and experimental design). Many such problems can be formulated as integer-programming packing or covering problems. Indeed, such formulations have been the most successful means of attacking many of these problems. Useful algorithmic and structural insights, which often have direct impact on our ability to solve practical instances of these problems, are achieved through the theories of integral polyhedra, graphs, hypergraphs, matroids and clutters. In particular, decomposition methods play a central role. Our project is a five-day conference, held at the University of Kentucky, devoted to this topic. The main activity of this conference is a series of ten lectures by Dr. Gerard Cornuejols of Carnegie Mellon University. The lectures will serve to introduce mathematicians (established researchers in discrete mathematics and in other areas, postdoctoral fellows and graduate students) to current research in packing and covering. This conference is particularly timely since the field has seen rapid development in the last several years, in terms of both theory and application.