 
Summary: ONLINE ALGORITHMS FOR PATH SELECTION IN A
NONBLOCKING NETWORK
SANJEEV ARORA , F. THOMSON LEIGHTON , AND BRUCE M. MAGGS §
Abstract.
This paper presents the first optimaltime algorithms for path selection in an optimalsize non
blocking network. In particular, we describe an Ninput, Noutput, nonblocking network with
O(N log N) boundeddegree 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.
Key words. nonblocking network, multibutterfly network, multiBenes network, routing algo
rithm
AMS subject classifications. 68M10, 90B12, 94C10
1. Introduction.
1.1. Definitions. Nonblocking networks arise in a variety of communications
contexts. Common examples include telephone systems and network architectures for
