A Parallel Approximation Algorithm for Positive Semidefinite Programming

Positive semi definite programs are an important subclass of semi definite programs in which all matrices involved in the specification of the problem are positive semi definite and all scalars involved are non-negative. We present a parallel algorithm, which given an instance of a positive semi definite program of size N and an approximation factor ε >; 0, runs in (parallel) time poly(1/ε)·polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1+ε) to the optimal. Our result generalizes analogous result of Luby and Nisan (1993) for positive linear programs and our algorithm is inspired by their algorithm of [10].