Research Initiation: Polyhedral Theory and Algorithms for Two NP-Complete Problems

在离散优化问题中，优先约束是经常出现的问题 问题 多面体理论和计算经验都表明 大部分由优先约束定义的整数程序 结构，可以利用开发良好的多面体为基础的 算法的解决方案。 两个重要的整数规划 有优先约束的问题是优先约束的 背包问题和工厂选址问题。 PI将开发 这些NP完全问题的新多面体结果， 与现有的多面体结果快速，有效的算法， 解决方案可以实现。 将特别注意 并行算法的发展。 除了提供业务 算法，可用于解决这两个实际应用 问题，工作将扩展已知的理论多面体 组合学

Precedence constraints arise frequently in discrete optimization problems. Polyhedral theory and computational experience both suggest that integer programs defined largely by precedence constraints have structure that can be exploited to develop good polyhedral-based algorithms for their solution. Two important integer programming problems with precedence constraints are the precedence-constrained knapsack problem and the plant location problem. The PI will develop new polyhedral results for these NP-complete problems so that together with existing polyhedral results fast, efficient algorithms for their solution can be implemented. Special attention will be given to the development of parallel algorithms. Beyond providing operational algorithms that can be used to solve actual applications of these two problems, the work will extend the known theory of polyhedral combinatorics.