On-Line Algorithms for Path Selection in a Nonblocking Network

Abstract

This paper presents the first optimal-time algorithms for path selection in an optimal-size nonblocking network. In particular, we describe an $N$-input, $N$-output, nonblocking network with $O(N \log N)$ bounded-degree nodes, and an algorithm that can satisfy any request for a connection or disconnection between an input and an output in $O(\log N)$ bit steps, even if many requests are made at once. Viewed in a telephone switching context, the algorithm can put through any set of calls among $N$ parties in $O(\log N)$ bit steps, even if many calls are placed simultaneously. Parties can hang up and call again whenever they like; every call is still put through $O(\log N)$ bit steps after being placed. Viewed in a distributed memory machine context, our algorithm allows any processor to access any idle block of memory within $O(\log N)$ bit steps, no matter what other connections have been made previously or are being made simultaneously.