Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word `separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

This book constitutes the proceedings of the First Annual International Conference on Computing and Combinatorics, COCOON '95, held in Xi'an, China in August 1995. The 52 thoroughly refereed full papers and the 22 short presentations included in this volume were selected from a total of 120 submissions. All current aspects of theoretical computer science and combinatorial mathematics related to computing are addressed; in particular, there are sections on complexity theory, graph drawing, computational geometry, databases, graph algorithms, distributed programming and logic, combinatorics, machine models, combinatorial designs, algorithmic learning, algorithms, distributed computing, and scheduling.

Recent work has shown that by considering an optimization perspective of the eigenvalues and eigenvectors of graph Laplacians, more efficient algorithms can be developed for tackling many graph-related computing tasks. In this dissertation, we present efficient methods for solving general quadratic programs with nonconvex constraints in the context of very-large-scale integration (VLSI) computer-aided design (CAD) and graph-based semi-supervised learning problems. We propose a general framework for matrix quadratic programming with nonconvex constraints, which is motivated by classic algorithms for solving trust-region subproblems. We introduce approximate and iterative methods with derived convergence guarantees. We demonstrate the effectiveness of our framework on large-scale numerical test cases, specifically real-world benchmarks. By leveraging analytical VLSI and PCB layout engines, we show that effective initialization using our method consistently improves a variety of pre- and post-detailed placement metrics. Additionally, we introduce a graph semi-supervised learning algorithm based on this framework, which yields strong results across a wide spectrum of label rates.

This volume gives the proceedings of WG '90, the 16th in a series of workshops. The aim of the workshop series is to contribute to integration in computer science by applying graph-theoretic concepts. The workshops are unusual in that they combine theoretical aspects with practice and applications. The volume is organized into sections on: - Graph algorithms and complexity, - VLSI layout, - Multiprocessor systems and concurrency, - Computational geometry, - Graphs, languages and databases, - Graph grammars. The volume contains revised versions of nearly all the papers presented at the workshop. Several papers take the form of preliminary reports on ongoing research.