The multi-stripe travelling salesman problem

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q ≥ 1, the objective function sums the costs for travelling from one city to each of the next q cities along the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polyomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP

A new family of scientific impact measures : the generalized Kosmulski-indices

This article introduces the generalized Kosmulski-indices as a new family of scientific impact measures for ranking the output of scientific researchers. As special cases, this family contains the well-known Hirsch-index h and the Kosmulski-index h ((2)). The main contribution is an axiomatic characterization that characterizes every generalized Kosmulski-index in terms of three axioms

Minimum-weight double-tree shortcutting for Metric TSP: Bounding the approximation ratio ✩

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e. the minimum-weight double-tree shortcutting. Previously, we gave an efficient algorithm for this problem, and carried out its experimental analysis. In this paper, we address the related question of the worst-case approximation ratio for the minimum-weight double-tree shortcutting method. In particular, we give lower bounds on the approximation ratio in some specific metric spaces: the ratio of 2 in the discrete shortest path metric, 1.622 in the planar Euclidean metric, and 1.666 in the planar Minkowski metric. The only known upper bound is 2, which holds trivially in any metric space. We conjecture that for the Euclidean and Minkowski metrics, the upper bound can be improved to match our lower bounds. 1

Group up to learn together: a system for equitable allocation of students to groups

Group-based learning is overwhelmingly accepted as an important feature of current education practices. The success of using a group-based teaching methodology depends, to a great extent, on the quality of the allocation of students into working teams. We have modelled this problem as a vector packing problem and constructed an algorithm that combines the advantage of local search algorithms with the branch and bound methodology. The algorithm easily finds exact solutions to real life problems with about 130-150 students. The algorithm is implemented in GroupUp - a decision support tool which has been successfully used in the University of Warwick for a number of years

Well-Solvable Special Cases of the TSP: A Survey

The Traveling Salesman Problem belongs to the most important and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently. We survey these special cases with emphasis on results obtained during the decade 1985--1995. This survey complements an earlier survey from 1985 compiled by Gilmore, Lawler and Shmoys