In 1975, Kalmanson proved that if the distance matrix in the travelling salesman problem (TSP) fulfills certain combinatorial conditions (that are nowadays called the Kalmanson conditions) then the TSP is solvable in polynomial time [Canad. J. Math., 27 (1995), pp. 1000– 1010]. We deal with the problem of deciding, for a given instance of the TSP, whether there is a renumbering of the cities su...

In this paper, we introduce the 1− K robotic-cell scheduling problem, whose solution can be reduced to solving a TSP on specially structured permuted Monge matrices, we call b-decomposable matrices. We also review a number of other scheduling problems which all reduce to solving TSP-s on permuted Monge matrices. We present the important insight that the TSP on b-decomposable matrices can be sol...

Let the edges of the complete graph Kn be assigned independent uniform [0; 1] random edge weights. Let ZTSP and Z2FAC be the weights of the minimum length travelling salesman tour and minimum weight 2-factor respectively. We show that whp jZTSP Z2FAC j = o(1). The proof is via by the analysis of a polynomial time algorithm that nds a tour only a little longer than Z2FAC .

It is known that the performance of a genetic algorithm depends on the survival environment and the reproducibility of building blocks. In this paper, we propose a new encoding/crossover scheme that uses genic distance which explicitly defines the distance between each pair of genes in the chromosome. It pursues both relatively high survival probabilities of more epistatic gene groups and diver...

This paper presents a decomposition algorithm for solving the uniform Travelling Salesman Problem (TSP). The algorithm assumes that the initial set of points is divided into subsets and overlapping regions between these subsets. The algorithm starts by considering a subset and find the solution in that subset. The solution in the next subset is calculated by expanding the earlier solution for t...

In this study, we experimentally investigate collaborative scientific activities that are undertaken through a virtual space such as the Internet. In such cases, a partner has two aspects: an imaginary partner with whom the problem solver seems to work together, and an actual partner with whom he/she actually works. We design an experimental environment in which we can control the two factors i...

The Traveling Salesman Problem (TSP) is a classical problem in discrete optimization. Its paradigmatic character makes it one of the most studied in computer science and operations research and one for which an impressive amount of algorithms (in particular heuristics and approximation algorithms) have been proposed. While in the general case the problem is known not to allow any constant ratio...

The recent theoretical discovery of families of travelling wave solutions in pipe flow (Faisst & Eckhardt 2003; Wedin & Kerswell 2004; Hof et al. 2004) at Reynolds numbers lower than the transitional range naturally raises the question of their relevance to the turbulent transition process. Here a series of numerical experiments are conducted in which we look for the spatial signature of these ...

Internationally, the population is ageing and people are living well, longer. In Australia, extended travelling has gained popularity among older Grey Nomads due to time and opportunity post retirement. However, there is limited research available focusing on older Australians' health while travelling. This paper reports the qualitative phase of a larger mixed-method project that explores the e...