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
Least majorized elements and generalized polymatroids
Mathematics of Operations Research
Convergence complexity of optimistic rate-based flow-control algorithms
Journal of Algorithms
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Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
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Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Using approximate majorization to characterize protocol fairness
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Fairness in routing and load balancing
Journal of Computer and System Sciences - Special issue on Internet algorithms
Combining fairness with throughout: online routing with multiple objectives
Journal of Computer and System Sciences - Special issue on Internet algorithms
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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
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
Fairness measures for resource allocation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximate majorization and fair online load balancing
ACM Transactions on Algorithms (TALG)
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Bandwidth allocation in networks: a single dual update subroutine for multiple objectives
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Bi-objective Optimization: An Online Algorithm for Job Assignment
GPC '09 Proceedings of the 4th International Conference on Advances in Grid and Pervasive Computing
User utility discovery for priority-based network resource pricing
Computers and Industrial Engineering
Mesh-based peer-to-peer layered video streaming with taxation
Proceedings of the 20th international workshop on Network and operating systems support for digital audio and video
ACM Transactions on Algorithms (TALG)
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In this paper, we present a simple distributed algorithm for resource allocation which simultaneously approximates the optimum value for a large class of objective functions. In particular, we consider the class of canonical utility functions U that are symmetric, non-decreasing, concave, and satisfy U(0) = 0. Our distributed algorithm is based on primal-dual updates. We prove that this algorithm is an O(log ρ)-approximation for all canonical utility functions simultaneously, i.e. without any knowledge of U. The algorithm needs at most O(log2 ρ) iterations. Here n is the number of flows, m is the number of edges, R is the ratio between the maximum capacity and the minimum capacity of the edges in the network, and ρ is max (n, m, R).We extend this result to multi-path routing, and also to a natural pricing mechanism that results in a simple and practical protocol for bandwidth allocation in a network. When the protocol reaches equilibrium, the allocated bandwidths are the same as when the distributed algorithm converges; hence the protocol is also an O(log ρ) approximation for all canonical utility functions.