Asynchronous Organizations for Solving the Point-to-Point Connection Problem Fernando de Carvalho Gomes Laborat´ orio de Inteligˆ encia Artificial - LIA Universidade Federal do Cear´ a Fortaleza - CE, Brazil carvalho@lia.ufc.br Cl´ audio Nogueira de Meneses Institute of Computing State University of Campinas Campinas - SP - Brazil nogueira@dcc.unicamp.br Allan G. Lima and Carlos S. Oliveira Computer Science Department State University of Ceara Fortaleza - CE, Brazil, allan,carlos @uece.br Abstract We present an agent approach to solve the nonfixed point-to-point connection problem. The optimization ver- sion of this problem is NP-hard and has numerous applica- tions in circuit switching and VLSI design. We use Asyn- chronous Teams (or A-Teams) technique to search for an optimal global solution. An A-Team is an organization of agents that communicate with each other by means of shared memories. Each agent is a heuristic strategy that can make its own choices about its inputs, scheduling and resource allocation. Computational results comparing our approach with an exact algorithm proposed by Meneses are presented. 1 Introduction We are concerned with providing a near optimal global solution to the nonfixed point-to-point connection (PPC) problem, in an acceptable amount of computation time. The PPC problem is defined as follows: let be an undirected connected graph, , , be source vertices, be destination vertices, , and a nonnegative integral weight (or length) for each edge . We want to find a minimum point-to-point connection, i.e., a subset such that each source- destination pair is connected by a path using only edges in , and is minimum. In the Figure 1 we show an instance of the PPC problem. This problem and its variations have numerous applica- Source Vertex e Destination Vertex 2 2 3 3 5 1 2 10 15 1 4 4 9 7 a b c d h g f (a) Source Vertex e Destination Vertex 2 2 3 3 5 1 2 10 15 1 4 4 9 7 a b c d h g f (b) Figure 1. (a) An instance of the PPC problem. In (b) the edge set represents a solution to the instance in (a). An alternative solution to this instance is given by edge set . tions in circuit switching and VLSI design [8]. There exist polynomial time dynamic programming al- gorithms for solving point-to-point connection instances, where the number of source-destination pairs ( ) is no greater than 3. In real world applications we need to solve far larger problem instances, i.e., presenting many source- destination pairs. Another objective in this work is to show how differents agents can be combined, in order to obtain better solutions than will obtained by these agents alone. To show this we design some simple agents that cooperate to produce good solutions. These agents are organized as an Asynchronous Team (A-Team). An A-Team is an organization of agents that communicate with each other by means of shared mem- ories. Each agent is a heuristic strategy that can make its