# 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. © 1990.