40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039) (1999)
New York, New York
Oct. 17, 1999 to Oct. 18, 1999
Jon Kleinberg , Cornell University
Eva Tardos , Cornell University
Yuval Rabani , Technion - Israel Institute of Technology
We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria interacts in a complex fashion with the optimization of network utilization and throughput; in this work, we undertake an investigation of this relationship through the framework of approximation algorithms.In a range of settings including both high-speed networks and Internet applications, max-min fairness has emerged as a widely accepted formulation of the notion of fairness. Informally, we say that an allocation of bandwidth is max-min fair if there is no way to give more bandwidth to any connection without decreasing the allocation to a connection of lesser or equal bandwidth. Given a collection of transmission routes, this criterion imposes a certain equilibrium condition on the bandwidth allocation, and some simple flow control mechanisms converge quickly to this equilibrium state. Indeed, the vast majority of previous work on max-min fairness has focused on this issue of associating rates with connections that are specified by a fixed set of paths. Very little work has been devoted to understanding the relationship between the way in which one selects paths for routing, and the amount of throughput one obtains from the resulting max-min fair allocation on these paths.In this work we consider the problem of selecting paths for routing so as to provide a bandwidth allocation that is as fair as possible (in the max-min sense). We obtain the first approximation algorithms for this basic optimization problem, for single-source unsplittable routings in an arbitrary directed graph. Special cases of our model include several fundamental load balancing problems, endowing them with a natural fairness criterion to which our approach can be applied. Our results form an interesting counterpart to earlier work of Megiddo, who considered max-min fairness for single-source fractional flow. The optimization problems in our setting become NP-complete, and require the development of new techniques for relating fractional relaxations of routing to the equilibrium constraints imposed by the fairness criterion.
Network routing, max-min fairness, bandwidth allocation, maximum flow, unsplittable flow, load balancing
J. Kleinberg, E. Tardos and Y. Rabani, "Fairness in Routing and Load Balancing," 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)(FOCS), New York, New York, 1999, pp. 568.