Filipa Carvalho

Upper bounds and heuristics for the 2-club problem

Given an undirected graph G = (V, E), a k-club is a subset of V that induces a subgraph of diameter at most k. The k-club problem is that of finding the maximum cardinality k-club in G. In this paper we present valid inequalities for the 2-club polytope and derive conditions for them to define facets. These inequalities are the basis of a strengthened formulation for the 2-club problem and a cutting plane algorithm. The LP relaxation of the strengthened formulation is used to compute upper bounds on the problems optimum and to guide the generation of near-optimal solutions. Numerical experiments indicate that this approach is quite effective in terms of solution quality and speed, especially for low density graphs.

Integer models and upper bounds for the 3-club problem

Given an undirected graph, the k -club problem seeks a maximum cardinality subset of nodes that induces a subgraph with diameter at most k. We present two new formulations for the 3-club problem: one is compact and the other has a nonpolynomial number of constraints. By defining an integer compact relaxation of the second formulation, we obtain a new upper bound on the 3-club optimum that improves on the 3-clique number bound. We derive new families of valid inequalities for the 3-club polytope and use them to strengthen the LP relaxations of the new models. The computational study is performed on 120 graphs with up to 200 nodes and edge densities reported in the literature to produce difficult instances of the 3-club problem. The results show that the new compact formulation is competitive with the exact solution methods reported in the literature, and that a large proportion of the LP gap is bridged with the new valid inequalities.

Cell suppression problem: A genetic-based approach

Cell suppression is one of the most frequently used techniques to prevent the disclosure of sensitive data in statistical tables. Finding the minimum cost set of nonsensitive entries to suppress, along with the sensitive ones, in order to make a table safe for publication, is a NP-hard problem, denoted the cell suppression problem (CSP). In this paper, we present GenSup, a new heuristic for the CSP, which combines the general features of genetic algorithms with safety conditions derived by several authors. The safety conditions are used to develop fast procedures to generate multiple initial solutions and also to recombine, to perturb and to repair solutions in order to improve their quality. The results obtained for 300 tables, with up to more than 90,000 entries, show that GenSup is very effective at finding low-cost sets of complementary suppressions to protect confidential data in two-dimensional tables.

An analytical comparison of the LP relaxations of integer models for the k-club problem

Given an undirected graph G=(V,E), a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem is to find a maximum cardinality k-club. In this study, we use a linear programming relaxation standpoint to compare integer formulations for the k-club problem. The comparisons involve formulations known from the literature and new formulations, built in different variable spaces. For the case k=3, we propose two enhanced compact formulations. From the LP relaxation standpoint these formulations dominate all other compact formulations in the literature and are equivalent to a formulation with a non-polynomial number of constraints. Also for k=3, we compare the relative strength of LP relaxations for all formulations examined in the study (new and known from the literature). Based on insights obtained from the comparative study, we devise a strengthened version of a recursive compact formulation in the literature for the k-club problem (k>1) and show how to modify one of the new formulations for the case k=3 in order to accommodate additional constraints recently proposed in the literature.

Lower-bounding procedures for the 2-dimensional cell suppression problem

Abstract To protect confidential data from disclosure, statistical offices use a technique called cell suppression which consists of suppressing data from the statistical tables they publish. As some row and column subtotals are published, omitting just the confidential values does not guarantee in every case that they cannot be disclosed or estimated within a narrow range. Therefore to protect confidential data it is often necessary to make complementary suppressions, that is, to suppress also values that are not confidential. Assigning a cost to every complementary suppression, the cell suppression problem is that of finding a set of complementary suppressions with minimum total cost. In this paper new necessary protection conditions are presented. Combining these new conditions with the ones known from the literature new lower-bounding methods for the cell suppression problem are developed. Dominance theoretical results are proven and computational experience is reported for randomly generated tables.

Exact disclosure prevention in two-dimensional statistical tables

We propose new formulations for the exact disclosure problem and develop Lagrangian schemes, that rely on shortest path problems, to generate near optimal solutions. Computational experience is reported for 550 tables with up to 40,000 cells. A proven optimal solution was obtained for 95% of the instances and a near optimal solution was computed for each remaining instance as well as an upper bound on the deviation from the optimum.

Ergonomic Work Analysis of a Pathological Anatomy Service in a Portuguese Hospital

Awkward and uncomfortable postures when maintained for long periods of time could stress and fatigue supporting muscles and tendons, leading to the development of musculoskeletal disorders (MSD). An Ergonomic Work Analysis was required to assess and evaluate the working conditions in a pathological anatomy laboratory. The objectives of this study were: assess the actual working conditions of the professionals in that service; establish relationships between them and the complaints presented; identify and select the most painful task/workstation, characterize this task/workstation in terms of the associated MSD development risk and, finally, identify and propose some preventive measures. The Rapid Upper Limb Assessment was used and the results revealed that the risk for the development of MSD is present in all tasks. The three most critical tasks were identified. Considering the self-reported physical symptoms, the results were similar with the other studies reported.

The triangle k-club problem

Graph models have long been used in social network analysis and other social and natural sciences to render the analysis of complex systems easier. In applied studies, to understand the behaviour of social networks and the interactions that command that behaviour, it is often necessary to identify sets of elements which form cohesive groups, i.e., groups of actors that are strongly interrelated. The clique concept is a suitable representation for groups of actors that are all directly related pair-wise. However, many social relationships are established not only face-to-face but also through intermediaries, and the clique concept misses all the latter. To deal with these cases, it is necessary to adopt approaches that relax the clique concept. In this paper we introduce a new clique relaxation—the triangle k-club—and its associated maximization problem—the maximum triangle k-club problem. We propose integer programming formulations for the problem, stated in different variable spaces, and derive valid inequalities to strengthen their linear programming relaxations. Computational results on randomly generated and real-world graphs, with

Investigation of Musculoskeletal Symptoms and Associated Risk Factors in the HORECA Sector

k=2