Bandwidth Allocation in Networks: A Single Dual Update Subroutine for Multiple Objectives

Cho, Sung-woo; Goel, Ashish

doi:10.1007/11527954_4

“…This leaves open the following question: Can there be efficient distributed algorithms that achieve the same results? [Cho and Goel 2004] made some partial progress toward this problem by giving a centralized algorithm that maintains only one set of dual costs. Later, Cho and Goel [2006] presented a simple distributed algorithm-a simple protocol supported by prices that achieves the same result.…”

Section: Related Workmentioning

confidence: 99%

Price-based protocols for fair resource allocation

Goel

¹

,

Nazerzadeh

²

2014

ACM Trans. Algorithms

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3

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We analyze several distributed, continuous time protocols for a fair allocation of bandwidths to flows in a network (or resources to agents). Our protocols converge to an allocation that is a logarithmic approximation, simultaneously, to all canonical social welfare functions (i.e., functions that are symmetric, concave, and nondecreasing). These protocols can be started in an arbitrary state. Although a similar protocol was known before, it only applied to the simple bandwidth allocation problem, and its stability and convergence time were not understood. In contrast, our protocols also apply to the more general case of Leontief utilities, where each user may place a different requirement on each resource. Furthermore, we prove that our protocols converge in polynomial time. The best convergence time we prove is O(n log nc MAX a MAX c MIN a MIN ), where n is the number of agents in the network, c MAX and c MIN are the maximum and minimum capacity of the links, and a max , a min are respectively the largest and smallest Leontief coefficients. This time is achieved by a simple Multiplicative Increase, Multiplicative Decrease (MIMD) protocol that had not been studied before in this setting. We also identify combinatorial properties of these protocols that may be useful in proving stronger convergence bounds. The final allocations by our protocols are supported by usage-sensitive dual prices that are fair in the sense that they shield light users of a resource from the impact of heavy users. Thus, our protocols can also be thought of as efficient distributed schemes for computing fair prices. ACM Reference Format:Ashish Goel and Hamid Nazerzadeh. 2014. Price-based protocols for fair resource allocation: Convergence time analysis and extension to leontief utilities.

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“…This leaves open the following question: Can there be efficient distributed algorithms which achieve the same results? Cho and Goel [7] made some partial progress towards this problem by giving a centralized algorithm which maintains only one set of dual costs. However their single-dual algorithm was still inherently centralized and their techniques do not offer much insight towards obtaining the results in this paper.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…This was the approach taken in an earlier paper by Cho and Goel [7], but unfortunately, this approach did not lead to a distributed algorithm. In this paper, we present an algorithm that does not implement the dual subroutine at all; in fact the algorithm that we present in the next section is much simpler than using the above approach for even one prefix.…”

Section: The Following Theorem Is Also Immediate From [12]mentioning

confidence: 99%

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Pricing for Fairness: Distributed Resource Allocation for Multiple Objectives

Cho

¹

,

Goel

²

2010

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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(log 2 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.

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“…source-destination pairs) in a network (see [17,2,4,20,1,5,3,11,7] for some of the recent research on the problem). Apart from being important in its own right, this problem also models a wide variety of other resource allocation problems.…”

Section: Introductionmentioning

confidence: 99%

Pricing for fairness

Cho

¹

,

Goel

²

2006

Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing

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9

0

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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(log 2 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.

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Bandwidth Allocation in Networks: A Single Dual Update Subroutine for Multiple Objectives

Cited by 8 publications

References 14 publications

Price-based protocols for fair resource allocation

Price-based protocols for fair resource allocation

Pricing for Fairness: Distributed Resource Allocation for Multiple Objectives

Pricing for fairness

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