Upward Max-min Fairness

Emilie Danna, Avinatan Hassidim, Haim Kaplan, Alok Kumar, Yishay Mansour, Danny Raz, Michal Segalov

Research output: Contribution to journalArticlepeer-review


Often one would like to allocate shared resources in a fair way. A common and well-studied notion of fairness is Max-Min Fairness, where we first maximize the smallest allocation, and subject to that the second smallest, and so on. We consider a networking application where multiple commodities compete over the capacity of a network. In our setting, each commodity has multiple possible paths to route its demand (for example, a network using Multiprotocol Label Switching (MPLS) tunneling). In this setting, the only known way of finding a max-min fair allocation requires an iterative solution of multiple linear programs. Such an approach, although polynomial time, scales badly with the size of the network, the number of demands, and the number of paths, and is hard to implement in a distributed environment. More importantly, a network operator has limited control and understanding of the inner working of the algorithm. In this article we introduce Upward Max-Min Fairness, a novel relaxation of Max-Min Fairness, and present a family of simple dynamics that converge to it. These dynamics can be implemented in a distributed manner. Moreover, we present an efficient combinatorial algorithm for finding an upward max-min fair allocation. This algorithm is a natural extension of the well-known Water Filling Algorithm for a multiple path setting. We test the expected behavior of this new algorithm and show that on realistic networks upward max-min fair allocations are comparable to the max-min fair allocations both in fairness and in network utilization.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of the ACM
Issue number1
StatePublished - Mar 2017


  • Algorithms
  • C.2.4 [computer-communication networks]: distributed systems
  • Design
  • F.2.2 [analysis of algorithms and problem complexity]: nonnumerical algorithms and problems
  • Iterative exhaustive waterfill
  • Max min fairness
  • Multicommodity flow upward max min fair multicommodity flow
  • Performance
  • Waterfill


Dive into the research topics of 'Upward Max-min Fairness'. Together they form a unique fingerprint.

Cite this