**May 18, 11:00AM-12:00PM, EE Conference Room**

**Abstract:**
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 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. More importantly,
a network operator has limited control and understanding of the inner
working of the algorithm. Finally, this approach is inherently centralized
and cannot be implemented via a distributed protocol.

In this paper 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.
This work was done in Google jointly with:
E Danna, A. Hassidim, H. Kaplan, A. Kumar Y. Mansour , and M. Segalov. The paper was a Runner Up for the INFOCOM '12 Best Paper Award.

**Speaker Biography**:
Danny Raz received his doctoral degree from the Weizmann Institute of Science, Israel, in 1995. From 1995 to 1997 he was a post-doctoral fellow at the International Computer Science Institute, (ICSI) Berkeley, CA, and a visiting lecturer at the University of California, Berkeley. Between 1997 and 2001 he was a Member of Technical Staff at the Networking Research Laboratory at Bell Labs, Lucent Technologies. In October 2000, Danny Raz joined the faculty of the computer science department at the Technion, Israel. He served as the general chair of OpenArch 2000, TPC co-chair of MMNS 2007, TPC co-chair of IM2009, and was an Editor of the IEEE/ACM Transactions on Networking (ToN) and of JCN. His primary research interest is the theory and application of management related problems in IP networks and cloud computing.