Abstract. We consider the problem of planning a shortest tour through a collection of neighborhoods in the plane, where each neighborhood is a disk whose radius is an i.i.d. random variable drawn from a known probability distribution. This is a stochastic version of the classic travel-ing salesman

services leading to a set of interdependent capacitated traveling salesman tours. 1

We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of n points in IR d , where d 1 is a constant. In the algebraic computation tree model, the complexities of both these problems are shown to be \Theta(n log n

Abstract — This paper describes an effective approach to solve the inspection problem via colored traveling salesman tours. Given an environment with obstacles and regions to be inspected, the approach plans a collision-free and dynamically-feasible motion trajectory that enables the vehicle

This paper gives a partitioning scheme for the geometric, planar traveling salesman problem, under the Euclidean metric: given a set S of n points in the plane, find a shortest closed tour (path) visiting all the points. The scheme employs randomization, and gives a tour that can be expected

We consider the Ordered Cluster Traveling Salesman Problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of n points. The points are partitioned into K, K n, prespeci ed clusters. The vehicle must rst visit the points in cluster 1, then the points

Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)-approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes

Abstract. A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a commu-nication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to k out of a total of n wireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1+) approximated by only looking at a small subset of the input, which is of size O k

We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer

Let the edges of the complete graph K be assigned independent uniform [0, 1] ran- dom edge weights. Let Zrsp and Z2FAC be the weights of the minimum length trav- elling salesman tour and minimum weight 2-factor respectively. We show that whp IZTsP -- Z2FACI = o(1). The proof is via