US-France Cooperative Research: Analysis and Evaluation of Combinatorial Structures and Algorithms

[0230800 . Savage]这项为期三年的美法应用数学合作奖由北卡罗来纳州立大学的Carla D. Savage、Pawel Hitczenko和William Stewart以及凡尔赛大学的Sylvie Corteel和她的团队共同获得。该项目侧重于综合的方法来分析在应用中出现的组合算法。在许多应用中，有些问题的解决需要考察指数数量的可能性。目前解决这些问题的启发式方法需要花费大量时间。研究人员专注于另一种方法，即结合概率建模技术来解决组合问题。这些问题来自计算生物学、光网络中的路由、分布式和多处理器系统中的资源管理以及经典组合学等领域。目标有两个：(1)设计新的方法来解决概率和马尔可夫链组合中的经典问题；(2)开发一种综合的组合/算法/概率方法来解决单一领域的传统方法已被证明不足的应用问题。该奖项代表了美国方面向美国国家科学基金会和法国国家科学研究中心（CNRS）提出的联合提案。美国国家科学基金会将支付美国研究人员和研究生的旅费和生活费。CNRS将支持法国研究人员访问美国。美国学生将受益于国际研究团队的科学技术和经验交流。

0230800SavageThis three-year award for U.S.-France collaboration in applied mathematics involves Carla D. Savage, Pawel Hitczenko, and William Stewart of North Carolina State University and Sylvie Corteel and her team at the University of Versailles. The project focuses on an integrated approach to the analysis of combinatorial algorithms arising in applications. In many applications, there are problems whose solutions require examination of an exponential number of possibilities. The current heuristic approach to these problems requires much time. The investigators focus on an alternative approach that incorporates probabilistic modeling techniques for combinatorial problems. The problems are drawn from areas of computational biology, routing in optical networks, resource management in distributed and multiprocessor systems, and classical combinatorics. The objectives are twofold: (1) devise new methods to attack classical problems in combinatorics with probability and Markov chains; and (2) develop an integrated combinatorial/algorithmic/probabilistic approach to applied problems for which traditional methods from a single area have proved inadequate. This award represents the US side of a joint proposal to the NSF and the French National Center for Scientific Research (CNRS). NSF will cover travel funds and living expenses for the US investigators and graduate students. The CNRS will support the visits of the French researchers to the United States. US students will benefit from the exchange of scientific techniques and experience with an international research team.