Abstract: We consider a computer network, represented by a communication graph: each node represents a processor and the communication is done synchronously along the edges. Can such a network compute its own graph's properties? E.g., how hard is it to list all the triangles in the graph, to find its shortest cycle, or to compute all-pairs shortest paths?
We will give an introduction to the relevant computation models. Then, we will discuss some recent results showing how to solve these problems faster using algebraic techniques (based on a joint work with Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen and Jukka Suomela).