Stateless distributed gradient descent for positive linear programs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
An SDP primal-dual algorithm for approximating the Lovász-theta function
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Stateless near optimal flow control with poly-logarithmic convergence
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Distributed fractional packing and maximum weighted b-matching via tail-recursive duality
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Heuristic algorithms in computational molecular biology
Journal of Computer and System Sciences
Faster and simpler width-independent parallel algorithms for positive semidefinite programming
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Sublinear optimization for machine learning
Journal of the ACM (JACM)
Content placement via the exponential potential function method
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We give an approximation algorithm for packing and covering linear programs (linear programs with nonnegative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm (with high probability) computes feasible primal and dual solutions whose costs are within a factor of 1 + \varepsilon of OPT (the optimal cost) in time {\rm O}(n + (r + c)\log (n)/\varepsilon ^2 ). For dense problems (with r,c = {\rm O}(\sqrt n )) the time is {\rm O}(n + \sqrt n \log (n)/\varepsilon ^2 ) - linear even as \varepsilon\to 0. In comparison, previous Lagrangian-relaxation algorithms generally take at least \Omega (n\log (n)/\varepsilon ^2 ) time, while (for small \varepsilon) the Simplex algorithm typically takes at least \Omega (n\min (r,c)) time.