Graph expansion and communication complexity of algorithms

In joint work with Ballard, Demmel, and Schwartz, we showed the communication cost of algorithms (also known as I/O-complexity) to be closely related to the small-set expansion properties of the corresponding computation graphs. This graph expansion approach produces first lower bounds on the communication costs of Strassen's and other fast matrix multiplication algorithms. I will discuss both the general method and its concrete implementations.



University of California, Berkeley; Member, School of Mathematics