Data networks
A digital fountain approach to reliable distribution of bulk data
Proceedings of the ACM SIGCOMM '98 conference on Applications, technologies, architectures, and protocols for computer communication
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
The impact of multicast layering on network fairness
IEEE/ACM Transactions on Networking (TON)
Power Control is not Required for Wireless Networks in the Linear Regime
WOWMOM '05 Proceedings of the Sixth IEEE International Symposium on World of Wireless Mobile and Multimedia Networks
Maximin performance of binary-input channels with uncertain noise distributions
IEEE Transactions on Information Theory
On max-min fair congestion control for multicast ABR service in ATM
IEEE Journal on Selected Areas in Communications
Minimum energy mobile wireless networks
IEEE Journal on Selected Areas in Communications
Optimal power control, scheduling, and routing in UWB networks
IEEE Journal on Selected Areas in Communications
Lexicographically Minimum and Maximum Load Linear Programming Problems
Operations Research
Proactive surge protection: a defense mechanism for bandwidth-based attacks
SS'08 Proceedings of the 17th conference on Security symposium
Optimizing Multi-hop Queries in ZigBee Based Multi-sink Sensor Networks
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Existence and uniqueness of fair rate allocations in lossy wireless networks
IEEE Transactions on Wireless Communications
Proactive surge protection: a defense mechanism for bandwidth-based attacks
IEEE/ACM Transactions on Networking (TON)
Log-convexity of rate region in 802.11e WLANs
IEEE Communications Letters
A lexicographic optimization framework to the flow control problem
IEEE Transactions on Information Theory
An efficient wireless switching architecture
WTS'10 Proceedings of the 9th conference on Wireless telecommunications symposium
Realising max-min fairness in 802.11e mesh networks
ISWPC'10 Proceedings of the 5th IEEE international conference on Wireless pervasive computing
Max-min utility fair flow management for networks with route diversity
International Journal of Network Management
Utility max-min fair rate allocation for multiuser multimedia communications
MMM'11 Proceedings of the 17th international conference on Advances in multimedia modeling - Volume Part I
Lexicographical minimization of routing hops in telecommunication networks
INOC'11 Proceedings of the 5th international conference on Network optimization
No justified complaints: on fair sharing of multiple resources
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Decentralized proactive resource allocation for maximizing throughput of P2P Grid
Journal of Parallel and Distributed Computing
Fair sampling across network flow measurements
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
A fairness model for resource allocation in wireless networks
IFIP'12 Proceedings of the 2012 international conference on Networking
FairCloud: sharing the network in cloud computing
Proceedings of the ACM SIGCOMM 2012 conference on Applications, technologies, architectures, and protocols for computer communication
Max-min fairness in 802.11 mesh networks
IEEE/ACM Transactions on Networking (TON)
FairCloud: sharing the network in cloud computing
ACM SIGCOMM Computer Communication Review - Special october issue SIGCOMM '12
On-line fair allocations based on bottlenecks and global priorities
Proceedings of the 4th ACM/SPEC International Conference on Performance Engineering
SR-IOV based Virtual Network Sharing
Proceedings of the Second International Conference on Innovative Computing and Cloud Computing
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Max-min fairness is widely used in various areas of networking. In every case where it is used, there is a proof of existence and one or several algorithms for computing it; in most, but not all cases, they are based on the notion of bottlenecks. In spite of this wide applicability, there are still examples, arising in the context of wireless or peer-to-peer networks, where the existing theories do not seem to apply directly. In this paper, we give a unifying treatment of max-min fairness, which encompasses all existing results in a simplifying framework, and extend its applicability to new examples. First, we observe that the existence of max-min fairness is actually a geometric property of the set of feasible allocations. There exist sets on which max-min fairness does not exist, and we describe a large class of sets on which a max-min fair allo cation does exist. This class contains, but is not limited to the compact, convex sets of RN. Second, we give a general purpose centralized algorithm, called Max-min Programming, for computing the max-min fair allocation in all cases where it exists (whether the set of feasible allocations is in our class or not). Its complexity is of the order of N linear programming steps in RN, in the case where the feasible set is defined by linear constraints. We show that, if the set of feasible allocations has the free disposal property, then Max-min Programming reduces to a simpler algorithm, called Water Filling, whose complexity is much lower. Free disposal corresponds to the cases where a bottleneck argument can be made, andWater Filling is the general form of all previously known centralized algorithms for such cases. All our results apply mutatis mutandis to min-max fairness. Our results apply to weighted, unweighted and util-max-min and min-max fairness. Distributed algorithms for the computation of max-min fair allocations are outside the scope of this paper.