半正定规划的并行近似算法
A Parallel Approximation Algorithm for Positive Semidefinite Programming
摘要：
半正定规划是半定规划的一个重要子类，其中所有涉及问题的规范矩阵都是半正定的，所有涉及的标量都是非负的。给出了一个半正定规划的并行算法，该算法以N为例，逼近因子eps > 0，在poly（N）处理器上并行运行poly（1/eps）\cdot polylog（N），并输出一个在（1 + eps）乘性因子内的值到最优解.我们的结果推广了Luby和Nisan [1993]关于正线性规划的类似结果，我们的算法受到了他们算法的启发。
英文摘要：
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel algorithm, which given an instance of a positive semidefinite program of size N and an approximation factor eps > 0, runs in (parallel) time poly(1/eps) \cdot polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1 + eps) 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.
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