Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Greedy distributed optimization of multi-commodity flows
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Stateless distributed gradient descent for positive linear programs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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We develop a framework of distributed and stateless solutions for implicitly given packing linear programs, which are solved by multiple agents operating in a cooperative but uncoordinated manner. This is motivated by multi-commodity flow problems where flows can be split along possibly exponentially many paths. Compared to explicitly given packing LPs, the main challenge here lies in the exponentially (or even infinitely) many variables handled by a single agent. An efficient algorithm thus must identify a few "good" variables to update. Using a notion similar to the shortest-path-first-flow-decomposition, our algorithm discovers polynomially many variables to update in each iteration. We prove that after polynomially many rounds, the discovered variables support a near-optimal solution to the given packing LP.