Efficient Forest Data Structure for Evolutionary Algorithms Applied to Network Design

The design of a network is a solution to several engineering and science problems. Several network design problems are known to be NP-hard, and population-based metaheuristics like evolutionary algorithms (EAs) have been largely investigated for such problems. Such optimization methods simultaneously generate a large number of potential solutions to investigate the search space in breadth and, consequently, to avoid local optima. Obtaining a potential solution usually involves the construction and maintenance of several spanning trees, or more generally, spanning forests. To efficiently explore the search space, special data structures have been developed to provide operations that manipulate a set of spanning trees (population). For a tree with n nodes, the most efficient data structures available in the literature require time O(n) to generate a new spanning tree that modifies an existing one and to store the new solution. We propose a new data structure, called node-depth-degree representation (NDDR), and we demonstrate that using this encoding, generating a new spanning forest requires average time O(root n). Experiments with an EA based on NDDR applied to large-scale instances of the degree-constrained minimum spanning tree problem have shown that the implementation adds small constants and lower order terms to the theoretical bound.

The Environmental Theme in Representations and Practices of Family Health Professionals in the Municipality of Manaus - State of Amazonas/Brazil

There are abundant scientific evidences showing that the increased risk of exposure to diseases is a consequence of anthropogenic environmental changes. In the Family Health Strategy, tasks with a clear environmental focus are prescribed, indicating to the professional teams that they should consider these aspects in their health practices. The objective of this research was to study representations and practices of Family Health Professionals of Manaus - State of Amazonas, Northern Brazil - about environmental issues and their interface with public health. Data were collected by means of participant observation and semi-structured interviews, and the qualitative analysis was carried out through Content Analysis and Methodological Triangulation. The results showed that most professionals do not understand the environment in a systemic way, even though they recognize the great impact that environmental factors have on human health; as interventions, the educational practices follow traditional methodologies and focus on blaming the individual and on the simple transmission of knowledge; the professionals' relationship with the community is limited to personal and/or collective care. It is concluded that in order to the Family Health Strategy to contribute to restructure the system, it is essential to redirect this new health policy model so that it becomes effective as a social and environmental practice.