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 in order 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.
Bibliographical noteFunding Information:
1A preliminary version of this paper appears in ‘‘Proc. 40th IEEE Symp. Foundations of Computer Science’’. 2Supported in part by a David and Lucile Packard Foundation Fellowship, an ONR Young Investigator Award, NSF Faculty Early Career Development Award CCR-9701399, and BSF Grant 96-00402. 3Work at the Technion supported by BSF Grant 96-00402, Ministry of Science Contract 9480198, and by the Fund of the Promotion of Research at the Technion. 4Research partially supported by NSF Grant CCR-9700163, ONR Grant N00014-98-1-058, and BSF Grant 96-00402.