We show that calculating contact map overlap (a measure of similarity of protein structures) is NPhard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the rst approximation algorithms with guaranteed error bounds, and NPcompleteness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest. A

We consider graph compression in terms of graph families. In particular, we show that graphs of bounded genus can be compressed to O(n) bits, where n is the number of vertices. We identify a property based on separators that makes O(n)-bit compression possible for some graphs of bounded arboricity. 1 Introduction Graph representation as a data compression problem Lossless data compression is a process of representing a body of data by another body of data of smaller size from which the original data can be completely reconstructed. In the past thirty years a great deal of work has been done on the theory and practice of text compression (e.g., printed text or program source code) and of digitized data (e.g., voice or images). In fact, data compression has become a well-established subject in computer science, information theory, and communication theory. In contrast, very little has been done on compressing graphs. Since graphs are encountered everywhere and are often of very la...

BDDs (Binary Decision Diagrams) are often used to represent Boolean expressions in hardware synthesis, hardware and software verification and numerous other applica-tions. BDD computation, implemented using tree data structures with binary nodes, is inherently memory intensive, and therefore suffers from the von Neumann memory bottleneck. This thesis examines an approach which can speed up BDD computation through compression of the graphical structure, reducing the overhead of handling memory pointers, and thereby reducing memory access latency. The novel aspect of this work is that a compression technique is used which allows BDD computation directly on the compressed data without the overheads of compression and decompression. The need for such an approach is driven by technology in two ways: the increasing discrepancy between CPU and memory speeds, and the move towards larger (64 bit) memory architectures. The work applies graph enumeration techniques to classify graph topology using a structural identifier (SID) coding table, providing the basis for algorithms which generate compressed representations. The work uses these new representations to develop algorithms which can pre-calculate results for specific graph-traversal operations in Combination lookup tables (CLT). The work distinguishes itself from other methods of reducing BDD access latency, such as index based systems, by improving spatial locality and simplifying computation at the same time.