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. 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

It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for K-colorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability of a solution changes abruptly from near 0 to near 1. It is the high density of well-separated almost solutions (local minima) at this boundary that cause search algorithms to "thrash". This boundary is a type of phase transition and we show that it is preserved under mappings between problems. We show that for some P problems either there is no phase transition or it occurs for bounded N (and so bound...

TreadMarks is a distributed shared memory (DSM) system for standard Unix systems such as SunOS and Ultrix. This paper presents a performance evaluation of TreadMarks running on Ultrix using DECstation-5000/240's that are connected by a 100-Mbps switch-based ATM LAN and a 10-Mbps Ethernet. Our objective is to determine the efficiency of a user-level DSM implementation on commercially available workstations and operating systems. We achieved good speedups on the 8-processor ATM network for Jacobi (7.4), TSP (7.2), Quicksort (6.3), and ILINK (5.7). For a slightly modified version of Water from the SPLASH benchmark suite, we achieved only moderate speedups (4.0) due to the high communication and synchronization rate. Speedups decline on the 10-Mbps Ethernet (5.5 for Jacobi, 6.5 for TSP, 4.2 for Quicksort, 5.1 for ILINK, and 2.1 for Water), reflecting the bandwidth limitations of the Ethernet. These results support the contention that, with suitable networking technology, DSM is a...