Optimization Techniques for Clustering , Connectivity , and Flow Problems in Complex Networks FA 9550 - 08 - 1 - 0483 FA 9550 -

This project develops network-based optimization methods for solving problems arising in complex system analysis and wireless networking applications. The study of complex systems is of utmost importance for a number of diverse areas of science, engineering and society, including biochemistry, social sciences, epidemiology, transportation, and telecommunications. The project makes contributions to the state of the art of network-based techniques for data mining of complex systems and virtual backbone-based routing in wireless ad hoc networks. The research in this project focused around the following four major thrusts: (I) Theoretical analysis of new models of clusters in networks; (II) Investigating new approaches to virtual backbone-based routing in wireless networks; (III) Establishing techniques for theoretical analysis of heuristics for inapproximable problems and designing new metaheuristic approaches for the problems of interest; (IV) Developing new models and algorithms for robust optimization and decision making in complex networks under uncertainty. More specific contributions resulting from this project include: (I) Introducing and investigating a robust version of the concept of k-club in networks, which embeds the requirement of predefined vertex connectivity into lowdiameter structures; studying the maximum k-club and maximum quasi-clique problems from mathematical programming perspective. (II) Developing new approaches to forming a virtual backbone in wireless sensor networks by introducing and utilizing a new concept of a bottleneck connected dominating set, which help to address the energy-scarcity considerations; distributed algorithms for approximating a minimum bottleneck connected dominating set are proposed. (III) Providing a framework for theoretical analysis of heuristics for hard discrete optimization and for analysis of performance of algorithm portfolios; introducing a metaheuristic framework of variable objective search that can be used for discrete optimization problems with different mathematical programming formulations, including continuous formulations. (IV) Suggesting LP-based solution methods for network flow problems subject to multiple uncertain arc failures, as well as for rehabilitation and maintenance decisions related to transportation infrastructure.