This chapter surveys approximation algorithms for hard geometric problems. The problems
we consider typically take inputs that are point sets or polytopes in two-or three-dimensional …

Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms
and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical …

Let P be a set of n points on the euclidean plane. Let L s (P) and L m (P) denote the lengths
of the Steiner minimum tree and the minimum spanning tree on P, respectively. In 1968 …

The Steiner tree problem is one of the most important combinatorial optimization problems. It
has a long history that can be traced back to the famous mathematician Fermat (1601-1665) …

Задача Штейиера последнее десятилетие привлекает большое внимание
исследователей в области дискретной оптимизации. В работе дан краткий обзор …

Efficient methods to model and optimize the design of open‐cut mines have been known for
many years. The design of the infrastructure of underground mines has a similar potential for …

A family of finitely many continuous functions on a polytope X, namely (g/sub i/(x))/sub i in I/,
is considered, and the problem of minimizing the function f (x)= max/sub i in I/g/sub i/(x) on X …

Steiner Tree Problems Page 1 S Steiner Tree Problems Ke Su1, Bing Lu2, Huang Ngo3, Panos
M. Pardalos4, and Ding-Zhu Du5 1University of Texas at Dallas, Richardson, TX, USA …

The Steiner problem is to find a shortest network (tree) 5'in the plane R2 connecting a given
set X of n points. There is an algorithm due to Melzak [6] for finding such an S, however …

Optimization is of central importance in all sciences. Nature inherently seeks optimal
solutions. For example, light travels through the" shortest" path and the folded state of a …