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 …

A (Slightly) Improved Approximation Algorithm for Metric TSP Page 1 A (Slightly) Improved
Approximation Algorithm for Metric TSP Anna R. Karlin karlin@cs.washington.edu …

We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions.
For every fixed c> 1 and given any n nodes in ℛ2, a randomized version of the scheme finds …

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

We study the problem of finding shortest tours/paths for “lawn mowing” and “milling”
problems: Given a region in the plane, and given the shape of a “cutter”(typically, a circle or …

We present a polynomial time approximation scheme for Euclidean TSP in/spl Rfr//sup 2/.
Given any n nodes in the plane and/spl epsiv/> 0, the scheme finds a (1+/spl epsiv/) …

For some positive constant ϵ 0, we give a (3/2-ϵ 0)-approximation algorithm for the
following problem: given a graph G 0=(V, V 0), find the shortest tour that visits every vertex at …

We present a randomized polynomial time approximation scheme for Euclidean TSP in
R/sup 2/that is substantially more efficient than our earlier scheme (1996)(and the scheme of …

We demonstrate a new connection between fixed-parameter tractability and approximation
algorithms for combinatorial optimization problems on planar graphs and their …

The local tree-width of a graph G=(V, E) is the function ltw^ G: N-> N that associates with
every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph …