The problem of routing messages in networks is a central concern in the area of parallel computation. Numerous routing results have been established, most of them in either the packet routing model or the wormhole routing model. Recently, emerging technologies have motivated new routing models and problems to be considered.

Optical fiber networks have motivated new routing problems that have some similarities to problems in wormhole routing, but which also have connections to certain VLSI channel routing problems. Cellular telephones and personal communications systems have motivated interest in problems of routing in wireless networks, which contain underlying resource allocation problems for the assignment of radio frequencies.

In this talk, I will describe recent results in these two routing models --- optical and wireless --- with an emphasis on the combinatorial and graph-theoretic techniques that have been central to progress in these areas.

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1996-1997 Mathematics in High Performance Computing