### DIMACS Theory of Computing Seminar

Title: A Tale of Two Local Models of Computation

Speaker: Guy Even, Tel-Aviv University

Date: Wednesday, September 28, 2016 11:00am-12:00pm

Location: CoRE Bldg, Room 301, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms.

Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in \$\log^* n\$, where \$n\$ is the number of vertices of the input graph.

The recursive centralized local improvement technique by Nguyen and Onak is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching. The improvement is twofold: we reduce the number of rounds from \$O(\log n)\$ to \$O(\log^* n)\$ and our algorithms are deterministic.

Time permitting, a centralized local algorithm for generating random preferential attachment graphs will be presented. Per query, the algorithms uses polylogarithmic random bits, time, and space.

Talk based on joint work with Reut Levy, Moti Medina, Dana Ron, and Adi Rosen.