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

0230800萨维奇这个为期三年的美国奖-法国合作应用数学涉及卡拉D。北卡罗来纳州州立大学的萨维奇、帕维尔·希岑科和威廉·斯图尔特以及凡尔赛大学的西尔维·科蒂尔和她的团队。 该项目的重点是一个综合的方法来分析组合算法中出现的应用。 在许多应用中，有些问题的解决方案需要检查指数数量的可能性。 目前对这些问题的启发式方法需要很多时间。 调查人员专注于一种替代方法，结合概率建模技术的组合问题。 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，用概率和马尔可夫链来解决组合数学中的经典问题;（2）开发一种综合的组合/算法/概率方法来解决应用问题，因为单一领域的传统方法已经证明是不够的。该奖项代表了美国方面向NSF和法国国家科学研究中心（CNRS）提出的联合建议。 NSF将为美国研究人员和研究生提供旅费和生活费。 CNRS将支持法国研究人员访问美国。 美国学生将受益于与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.