Self-stabilization of dynamic systems assuming only read/write atomicity
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Self-stabilization by local checking and correction (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Locality in distributed graph algorithms
SIAM Journal on Computing
Linear programming without the matrix
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
On-Line End-to-End Congestion Control
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Global Optimization Using Local Information with Applications to Flow Control
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Constant-time distributed dominating set approximation
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Stabilizing Communication Protocols
Stabilizing Communication Protocols
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Greedy distributed optimization of multi-commodity flows
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Distributed network monitoring and multicommodity flows: a primal-dual approach
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Distributed algorithms for multicommodity flow problems via approximate steepest descent framework
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems
SIAM Journal on Computing
Beating Simplex for Fractional Packing and Covering Linear Programs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Fast load balancing via bounded best response
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Stateless near optimal flow control with poly-logarithmic convergence
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Stateless distributed algorithms for near optimal maximum multicommodity flows
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Brief announcement: Stateless distributed algorithms for generalized packing linear programs
Proceedings of the 28th ACM symposium on Principles of distributed computing
IEEE/ACM Transactions on Networking (TON)
Hi-index | 0.00 |
We develop a framework of distributed and stateless solutions for packing and covering linear programs, which are solved by multiple agents operating in a cooperative but uncoordinated manner. Our model has a separate "agent" controlling each variable and an agent is allowed to read-off the current values only of those constraints in which it has non-zero coefficients. This is a natural model for many distributed applications like flow control, maximum bipartite matching, and dominating sets. The most appealing feature of our algorithms is their simplicity and polylogarithmic convergence. For the packing LP max{cx | Ax = 0}, the algorithm associates a dual variable yi = exp[1ε * (Aix/bi -1)] for each constraint i and each agent j iteratively increases (resp. decreases) xj multiplicatively if AjT y is too small (resp. large) as compared to cj. Our algorithm starting from a feasible solution, always maintains feasibility, and computes a (1+epsilon) approximation in poly((ln (mn A_max))ε) rounds. Here m and n are number of rows and columns of A and A_max, also known as the "width" of the LP, is the ratio of maximum and minimum non-zero entries Aij/(bicj). Similar algorithm works for the covering LP min{by | AT y = c, y = 0} as well. While exponential dual variables are used in several packing/ covering LP algorithms before [25, 9, 13, 12, 26, 16], this is the first algorithm which is both stateless and has polylogarithmic convergence. Our algorithms can be thought of as applying distributed gradient descent/ascent on a carefully chosen potential. Our analysis differs from those of previous multiplicative update based algorithms and argues that while the current solution is far away from optimality, the potential function decreases/increases by a significant factor.