Pseudo-determinism for Graph Streaming Problems
Given a fixed input for a search problem, pseudo-deterministic algorithms produce the same answer over multiple independent runs, with high probability. For example, we can efficiently find a certificate for inequality of multivariate polynomials pseudo-deterministically, but it is not known how to do so deterministically. The same notion can be extended to the streaming model. The problem of finding a nonzero element from a turnstile stream is previously shown to require linear space for both deterministic and pseudo-deterministic algorithms. Another model of streaming problems is that of graphs, where edge insertions and deletions occur along a stream. Some natural problems include connectivity, bipartiteness, and colorability of a graph. While the randomized and deterministic graph streaming algorithms have been mostly well-studied, we investigate pseudo-deterministic space lower bounds and upper bounds for graph theoretic streaming problems.
Joint work with Albert Gao, Andrew Caosun, Puhua Cheng for the course project of 15-859CC Algorithms for Big Data.