This proposal from Rutgers University, in cooperation with Princeton University, AT&T Bell Laboratories (Bell Labs), and Bell Communications Research (Bellcore), requests funds to establish a Science and Technology Center for Discrete Mathematics and Theoretical Computer Science. The Director of the Center will be Professor Daniel Gorenstein of Rutgers University. The Center in Discrete Mathematics and Theoretical Computer Science will strengthen the development of these two overlapping areas by focussing research activity in a continuing series of year-long research programs, workshops and conferences. Approximately seventy researchers from the four collaborating institutions provide the background coherence and direction for this activity. The core of the research activity will be carried out by a vigorous program of visitors (both senior and junior) from other institutions (academic, industrial, government laboratory). Postdoctoral fellows and graduate students will be affiliated with the Center for varying lengths of time. Each year the Center will designate specific areas for special attention, inviting leading experts in the designated fields to organize a research program in those areas of concentration. These areas will be chosen to take advantage of the expertise of the participating personnel from the collaborating institutions while addressing questions of demonstrable interest to researchers in both the discrete mathematics and theoretical computer science communities. Within these general guidelines, there are several avenues of potential emphasis that involve both serious theoretical inquiry and relevant application. For example, our modern "information society" depends on clear, efficiently designed and reliable telecommunications and communications systems. These are easily described by network theory and can be modeled using linear programming techniques. Transportation problems require similar techniques; and optimization and linear programming, possibly enhanced by parallel computations, are critical in VLSI design and manufacture. Discrete and computational geometry are foundational disciplines for computer graphics and robotics. As the geometries required for the applications become increasingly more complex, research in computational geometry becomes ever more important. Yet there are fundamental questions in discrete and computational geometry that must be addressed before the applications can be realized.
