Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

The Geometric Maximum Traveling Salesman Problem

We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n^{f-2} log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n^2 log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NP-hard. Our approach can be extended to the more general case of quasi-norms with not necessarily symmetric unit ball, where we get a complexity of O(n^{2f-2} log n). For the special case of two-dimensional metrics with f=4 (which includes the Rectilinear and Sup norms), we present a simple algorithm with O(n) running time. The algorithm does not use any indirect addressing, so its running time remains valid even in comparison based models in which sorting requires Omega(n \log n) time. The basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms. Complementing the results on simplicity for polyhedral norms, we prove that for the case of Euclidean distances in R^d for d>2, the Maximum TSP is NP-hard. This sheds new light on the well-studied difficulties of Euclidean distances.Comment: 24 pages, 6 figures; revised to appear in Journal of the ACM. (clarified some minor points, fixed typos

First in Village or Second in Rome

Though individuals prefer to join groups with high quality peers, there are also advantages from being high up in the pecking order within the group. We show that sorting of agents in this environment results in an overlapping interval structure in the type space. Segregation and mixing coexist in a stable equilibrium. A greater degree of egalitarianism within organizations leads to greater segregation across organizations. Policies that are effective for lower-quality organizations to attract talent may be counterproductive for higher-quality organizations to retain talent. The degree and the pattern of segregation are shown to depend also on whether higher types are less concerned with relative ranking within the organization, on relative size of organizations, and on the extent of idiosyncratic preferences for other organizational attributes.

Is Britain Pulling Apart? Area Disparities in Employment, Education and Crime

This paper explores the changing extent of concentration worklessness and deprivation in Britains communities over the last twenty years and seeks to identify what shapes patterns of relative affluence and deprivation. The paper goes on to explore the evidence that there are lasting consequences from concentrated deprivation for the residents, including children. The paper address issues of employment, educational outcomes and crime victimisation. Looking at the available evidence from the UK and abroad, the evidence suggests that concentrated deprivation has little effect on employment opportunities, (e.g. moving people to more affluent neighbourhoods would make little difference), has modest effects on childrens educational outcomes and propensity to get involved in deviant behaviours but substantial effects on crime victimisation. The paper then concludes on what policy agendas could be developed to address concentrated deprivation and above all its consequences on residents outcomes.neighbourhoods, employment, education, crime

Image quality assessment for iris biometric

Iris recognition, the ability to recognize and distinguish individuals by their iris pattern, is the most reliable biometric in terms of recognition and identification performance. However, performance of these systems is affected by poor quality imaging. In this work, we extend previous research efforts on iris quality assessment by analyzing the effect of seven quality factors: defocus blur, motion blur, off-angle, occlusion, specular reflection, lighting, and pixel-counts on the performance of traditional iris recognition system. We have concluded that defocus blur, motion blur, and off-angle are the factors that affect recognition performance the most. We further designed a fully automated iris image quality evaluation block that operates in two steps. First each factor is estimated individually, then the second step involves fusing the estimated factors by using Dempster-Shafer theory approach to evidential reasoning. The designed block is tested on two datasets, CASIA 1.0 and a dataset collected at WVU. (Abstract shortened by UMI.)

Spartan Daily, May 9, 1994

Volume 102, Issue 64https://scholarworks.sjsu.edu/spartandaily/8564/thumbnail.jp