Guest Editor’s Foreword: Algorithms, Combinatorics, & Geometry

Abstract

Knowledge of mathematics and combinatorics is central to the design of combinatorial algorithms. In addition, applications-related concepts may also give rise to interesting mathematical problems, or may even be used to solve mathematical problems. The workshop on Algorithms, Combinatorics, and Geometry (ACG) was held during November 29–December 1, 2007, at the University of North Texas (UNT), Denton, Texas. The ACG workshop was intended to provide a deeper understanding of some important concepts which are fundamental to different disciplines, and to bring together researchers in different areas of discrete mathematics and computer science and provide an opportunity for them to interact. The ACG workshop did not have a proceedings, but an abstract for each talk was posted online. See acg.unt.edu for details. This special issue of Algorithmica presents a collection of 10 invited papers which are related to the main theme of the workshop. Preliminary versions of some of these papers may have been published in conferences. Nonetheless, all papers appearing in this issue have been thoroughly refereed and are revised so that they are in a suitable form for publication in Algorithmica. We have included papers that cover a broad range of important concepts which are of interest to researchers in graph theory and graph algorithms, combinatorial and computational geometry, computer security, graph drawing, and randomized algorithms. While the main results in some papers may appear purely structural, all results have computational consequences. Cabello and Mohar study the crossing number problem for those graphs that become planar after removal of one edge. They develop min-max formulas, and hence, efficiently computable lower and upper bounds that give rise to approximation algorithms that improve the best known previous results.