CS Forum: Michael Elkin, Ben-Gurion University of the Negev

CS department's public guest lecture on 'Hopsets with Constant Hopbound, and Applications to Approximate Shortest Paths'. Lecture is open to everyone.

Speaker: Prof Michael Elkin
Speaker affiliation:
Ben-Gurion University of the Negev
Host: Prof Jukka Suomela
Time: 13:15 (coffee at 13:00)
Venue: AS1,TUAS building

Hopsets with Constant Hopbound, and Applications to Approximate Shortest Paths

Abstract

A $(\beta,\eps)$-hopset for a weighted undirected $n$-vertex graph $G=(V,E)$ is a set of edges, whose addition to the graph guarantees that every pair of vertices has a path between them that contains at most $\beta$ edges, whose length is within $1+\eps$ of the shortest path. In her seminal paper, Cohen [Coh00, JACM 2000] introduced the notion of hopsets in the context of parallel computation of approximate shortest paths, and since then it has found numerous applications in various other settings, such as dynamic graph algorithms, distributed computing, and the streaming model.

Cohen [Coh00] devised efficient algorithms for constructing hopsets with polylogarithmic in $n$ number of hops. Her constructions remain the state-of-the-art since the publication of her paper in STOC'94, i.e., for more than two decades.

In this work we exhibit the first construction of sparse hopsets with a constant number of hops. We also find efficient algorithms for hopsets in various computational settings, improving the best known constructions. Generally, our hopsets strictly outperform the hopsets of [Coh00], both in terms of their parameters, and in terms of the resources required to construct them.

We demonstrate the applicability of our results for the fundamental problem of computing approximate shortest paths from $s$ sources. Our results improve the running time for this problem in the parallel, distributed and streaming models, for a vast range of $s$.

The talk will be self-contained. In particular, we won't assume any prior knowledge about hopsets.

Joint work with Ofer Neiman.

Bio

Michael Elkin finished his B.Sc. in 1995 in Computer Science and Mathematics in Hebrew University. He then proceeded to a graduate program in Weizmann Institute of Science, where he completed a Ph.D. in Computer Science in 2002. After spending two years (2002-2003, 2003-2004) as a postdoctoral associate in Princeton, Institute for Advanced Study, School of Mathematics, and in Yale University, Computer Science department, respectively, he joined the Computer Science department of the Ben-Gurion University of the Negev as a faculty member. He serves in this capacity since then.