The power of multimedia: Combining point-to-point and multiaccess networks

Abstract

This paper introduces a new network model called a multimedia network . It combines the point-to-point message passing network and the multiaccess channel. To benefit from the combination, the designed algorithms consist of two stages: a local stage which utilizes the parallelism of the point-to-point network and a global stage which utilizes the broadcast capability of the multiaccess channel. To balance the complexities of the two stages a partition of the network into O( n ) connected components each of radius O( n ) is required. We present efficient deterministic and randomized partitioning algorithms that run in ( n log ∗ n ) time. The deterministic algorithm sends O(m + n log n log ∗ n) messages, while the randomized algorithm sends only O(m + n log ∗ n) messages. ( n and m are the number of nodes and point-to-point links in the network.) The partitioning algorithms are then used to obtain: (1) O( n log n log ∗ n ) time deterministic and O( n log ∗ n ) time randomized algorithms for computing global sensitive functions, and (2) An O( n log n ) time deterministic algorithm for computing a minimum spanning tree. We give Ω(n) time lower bounds for computing global sensitive functions in both point-to-point and multiaccess networks, thus showing that the multimedia network is more powerful than both its separate components. Furthermore, we prove and Ω( n ) time lower bound for computing global sensitive functions in multimedia networks, thus leaving a small gap between our upper and lower bounds.