An introduction to parallel algorithms
An introduction to parallel algorithms
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Efficient approximation algorithms for semidefinite programs arising from MAX CUT and COLORING
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An elementary proof of a theorem of Johnson and Lindenstrauss
Random Structures & Algorithms
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Beating Simplex for Fractional Packing and Covering Linear Programs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Efficient algorithms using the multiplicative weights update method
Efficient algorithms using the multiplicative weights update method
Distributed and parallel algorithms for weighted vertex cover and other covering problems
Proceedings of the 28th ACM symposium on Principles of distributed computing
Approximating Semidefinite Packing Programs
SIAM Journal on Optimization
A Parallel Approximation Algorithm for Positive Semidefinite Programming
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Feasible and accurate algorithms for covering semidefinite programs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Hi-index | 0.00 |
This paper studies the problem of finding a (1+ε)-approximate solution to positive semidefinite programs. These are semidefinite programs in which all matrices in the constraints and objective are positive semidefinite and all scalars are non-negative. At FOCS'11, Jain and Yao gave an NC algorithm that requires O(t 1/ε13 log13 m log n) iterations on input n constraint matrices of dimension m-by-m, where each iteration performs at least Ω(mω) work since it involves computing the spectral decomposition. We present a simpler NC parallel algorithm that on input with n constraint matrices, requires O(1/ε4 log4 n log(1/ε)) iterations, each of which involves only simple matrix operations and computing the trace of the product of a matrix exponential and a positive semidefinite matrix. Further, given a positive SDP in a factorized form, the total work of our algorithm is nearly-linear in the number of non-zero entries in the factorization. Our algorithm can be viewed as a generalization of Young's algorithm and analysis techniques for positive linear programs (Young, FOCS'01) to the semidefinite programming setting.