TH3.R5.2

Distributed matrix multiplication with straggler tolerance using algebraic function fields

Adrián Fidalgo-Díaz, Umberto Martínez-Peñas, University of Valladolid, Spain

Session:
Distributed Computing: Matrix Multiplication

Track:
13: Coding for Computation and Storage

Location:
Omikron I

Presentation Time:
Thu, 11 Jul, 14:55 - 15:15

Session Chair:
Salim El Rouayheb, Rutgers
Abstract
The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and matdot codes are generalized by making use of algebraic function fields (i.e., algebraic functions over an algebraic curve) over a finite field. The construction of optimal solutions is translated to a combinatorial problem on the Weierstrass semigroups of the corresponding algebraic curves. Optimal or almost optimal solutions are provided. These have the same computational complexity per worker as classical polynomial and matdot codes, and their recovery thresholds are almost optimal in the asymptotic regime (growing number of workers and a fixed finite field).
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