New Directions in Approximation Algorithms

该提案寻求继续资助PI在近似算法的主要研究领域的工作。PI的研究小组以前的NSF资助的工作已经成功地制定和解决了几个有趣的近似问题，包括批量购买网络设计，$k$-最小生成树，组斯坦纳树和度有界的最小生成树问题。我们在这一领域的贡献包括数学规划放松的困难问题和新的方法来轮这样的放松使用确定性和随机舍入技术，以及新的问题formulations. This建议的重点是解决的解决方案计算困难的问题在静脉的近似算法通过移动更接近现实世界的约束。具体来说，我们提出的工作方向包括将集成，异质性，竞争，不确定性和混合输入模型到经典问题。该提案报告了在每一个方向上取得的初步成功和正在进行的调查，并提出了具体的新问题和办法。该提案的智力价值是推动近似算法的前沿，扩大其范围和适用性，以及发现新的潜在技术的潜力。该提案辅之以教育和推广计划，继续PI参与更广泛的教育目标，如参与调查，辅导和教学研讨会，以及新课程和讲义的开发。该提案的更广泛的影响包括研究生培训和安置在这一研究领域，以及广泛的教育计划，旨在增加传播PI的研究，以更广泛的受众，包括四年制大学讲师。

This proposal seeks continued funding for the PI's work in his principal research area of Approximation Algorithms. Previous NSF-funded work by the PI's research group has successfully formulated and solved several interesting problems for approximation including the Buy-at-Bulk Network Design, $k$-Minimum Spanning Tree, Group Steiner Tree, and the Degree-bounded Minimum Spanning Tree problems. Our contributions to this area include mathematical programming relaxations of hard problems and novel ways to round such relaxations using deterministic and randomized rounding techniques, as well as new problem formulations.The focus of this proposal is to address the solution of computationally hard problems in the vein of approximation algorithms by moving closer to more real-world constraints.Specifically, we propose work in directions involving incorporating integration, heterogeneity, competition, uncertainty, and hybrid input models into classical problems. The proposal reports on preliminary successes and ongoing investigation in each of these directions, and formulates specific new problems and approaches. The intellectual merit of the proposal is to push the frontiers of approximation algorithms in terms of expanding its scope and applicability, as well as the potential for discovery of new underlying techniques.The proposal is complemented with an educational and outreach plan that continues the PI's involvement in broader educational goals such as participation in surveys, tutorials and teaching workshops, as well as new course and lecture note development. Thebroader impact of the proposal include graduate student training and placement in this research area as well as an extensive education plan aimed at increased dissemination of the PI's research to a broader audience including four-year college lecturers.