This award provides support for the Seventh International Conference on Random Structures and Algorithms which will be held in Atlanta on May 16-20, 1995. The aim of this meeting is to present recent research, and to identify and explore new directions for further development, in random discrete structures, randomized algorithms and broad areas of application of probabilistic methods in discrete mathematics and computer science. In addition to the intrinsic interest of the mathematics, these fields have numerous applications to such subjects as the reliability of communication, neural networks, percolation and polymerization processes, and sequencing DNA. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete sets of objects, and this makes use of combinatorial research.