Guest editors’ foreword

The 26th International Symposium on Algorithms and Computation (ISAAC 2015)\u3cbr/\u3ewas held in Nagoya, Japan, December 9–11, 2015. The program committee received\u3cbr/\u3e180 high-quality submissions, and 65 were accepted for presentation. This special\u3cbr/\u3eissue gathers a selection of six of these accepted papers, which went through the\u3cbr/\u3estandard refereeing process of the International Journal on Computational Geometry\u3cbr/\u3eand Applications

Approximation algorithms for the Euclidean traveling salesman problem with discrete and continuous neighborhoods

In the Euclidean traveling salesman problem with discrete neighborhoods, we are given a set of points P in the plane and a set of n connected regions (neighborhoods), each containing at least one point of P. We seek to find a tour of minimum length which visits at least one point in each region. We give (i) an O(a)-approximation algorithm for the case when the regions are disjoint and a-fat, with possibly varying size; (ii) an O(a3)-approximation algorithm for intersecting a-fat regions with comparable diameters. These results also apply to the case with continuous neighborhoods, where the sought TSP tour can hit each region at any point. We also give (iii) a simple O(log n)-approximation algorithm for continuous non-fat neighborhoods. The most distinguishing features of these algorithms are their simplicity and low running-time complexities