DOI: 10.1007/s002240010008 Theory Comput. Systems 34, 13–26 (2001) Theory of Computing Systems © 2001 Springer-Verlag New York Inc. Sharing Resources at Nonuniform Access Rates ∗ V. C. Barbosa, 1 M. R. F. Benevides, 1,2 and F. M. G. Fran¸ ca 1 1 Programa de Engenharia de Sistemas e Computa¸ c˜ ao, COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970 Rio de Janeiro - RJ, Brazil 2 Instituto de Matem´ atica, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970 Rio de Janeiro - RJ, Brazil Abstract. We introduce DPPr (for “Dining Philosophers Problem with rates”) as a generalization of the heavy-load case of the Dining Philosophers Problem (DPP). In DPPr, processes are required to be scheduled to access shared resources with prespecified relative frequencies. DPPr is an abstraction of resource-sharing problems to which the synchronization of some distributed algorithms for neural- network models and the generation of timing signals in asynchronous digital circuits are related. Two fully distributed, synchronous solutions are given for DPPr in this paper. The first solution employs a reduction to heavy-load DPP and after that a distributed scheduling mechanism that has been used to solve this problem with optimal concurrency. The second solution tackles the DPPr instance directly by operating on a multigraph based on that instance. We conclude by indicating how the two synchronous solutions carry over to the asynchronous case. 1. Introduction Let G be a connected undirected graph whose nodes represent processes and whose edges stand for the possibility of resource sharing between the processes that they connect. In the Dining Philosophers Problem (DPP) [5], [6], a process requires access to all resources it shares with all of its neighbors whenever it requires access to any resources, and, consequently, neighbors in G are precluded from accessing resources concurrently. One ∗ The authors have received partial support from the Brazilian agencies CNPq and CAPES, the PRONEX initiative of Brazil’s MCT under Contract 41.96.0857.00, and a FAPERJ BBP grant.