We present a refined construction of hierarchical probabilistic partitions with novel
properties, substantially stronger than previously known. Our construction provides a family …

We study exact algorithms for Euclidean TSP in R d. In the early 1990s algorithms with n O
(√ n) running time were presented for the planar case, and some years later an algorithm …

The traveling salesman problem (TSP) is a well studied NP-hard optimization problem. We
present a novel heuristic to find approximate solutions for the case of the TSP with Euclidean …

A chord is a straight line within a polygon connecting two non-adjacent vertices. Given such
a chord c of a polygon, we denote by n (c) the number of vertices visible from c. The chord …

Abstract We study the Traveling Salesman Problem inside a simple polygon. In this problem,
which we call tsp in a simple polygon, we wish to compute a shortest tour that visits a given …

In this paper, we study problems of connecting classes of points via noncrossing structures.
Given a set of colored terminal points, we want to find a graph for each color that connects …

In the Tricolored Euclidean Traveling Salesperson problem, we are given~ $ k= 3$ sets of
points in the plane and are looking for disjoint tours, each covering one of the sets. Arora …

In the Euclidean $ k $-TSP (resp. Euclidean $ k $-MST), we are given $ n $ points in the $ d
$-dimensional Euclidean space (for any fixed constant $ d\geq 2$) and a positive integer $ k …

In the Euclidean k-traveling salesman problem (k-TSP), we are given n points in the d-
dimensional Euclidean space, for some fixed constant d≥ 2, and a positive integer k. The …

The Traveling Salesman Problem (TSP) in the two-dimensional Euclidean plane is among
the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J …