Topics in matrix analysis
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
A new algorithm for minimizing convex functions over convex sets
Mathematical Programming: Series A and B
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
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating the cut-norm via Grothendieck's inequality
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
0(\sqrt {\log n)} Approximation to SPARSEST CUT in Õ(n2) Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies
INFORMS Journal on Computing
HAPLOFREQ: estimating haplotype frequencies efficiently
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Rank minimization via online learning
Proceedings of the 25th international conference on Machine learning
Sparse approximate solutions to semidefinite programs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Proceedings of the forty-second ACM symposium on Theory of computing
A note on element-wise matrix sparsification via a matrix-valued Bernstein inequality
Information Processing Letters
Journal of the ACM (JACM)
Efficient combination of probabilistic sampling approximations for robust image segmentation
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Feasible and accurate algorithms for covering semidefinite programs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A fast random sampling algorithm for sparsifying matrices
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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
A matrix hyperbolic cosine algorithm and applications
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Optimizing over the growing spectrahedron
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Efficient protocols for distributed classification and optimization
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
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Semidefinite programming (SDP) relaxations appear in many recent approximation algorithms but the only general technique for solving such SDP relaxations is via interior point methods. We use a Lagrangian-relaxation based technique (modified from the papers of Plotkin, Shmoys, and Tardos (PST), and Klein and Lu) to derive faster algorithms for approximately solving several families of SDP relaxations. The algorithms are based upon some improvements to the PST ideas-which lead to new results even for their framework - as well as improvements in approximate eigenvalue computations by using random sampling.