Emilie Jeanne Anne Danna

MIPLIB 2010 - Mixed Integer Programming Library version 5

This paper reports on the fifth version of the Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today’s codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.

A practical algorithm for balancing the max-min fairness and throughput objectives in traffic engineering

One of the goals of traffic engineering is to achieve a flexible trade-off between fairness and throughput so that users are satisfied with their bandwidth allocation and the network operator is satisfied with the utilization of network resources. In this paper, we propose a novel way to balance the throughput and fairness objectives with linear programming. It allows the network operator to precisely control the trade-off by bounding the fairness degradation for each commodity compared to the max-min fair solution or the throughput degradation compared to the optimal throughput. We also present improvements to a previous algorithm that achieves max-min fairness by solving a series of linear programs. We significantly reduce the number of steps needed when the access rate of commodities is limited. We extend the algorithm to two important practical use cases: importance weights and piece-wise linear utility functions for commodities. Our experiments on synthetic and real networks show that our algorithms achieve a significant speedup and provide practical insights on the trade-off between fairness and throughput.

Upward Max Min Fairness

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.

Upward Max-Min Fairness

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, which 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.

How to select a small set of diverse solutions to mixed integer programming problems

Given an oracle that generates a large number of solutions to mixed integer programs, we present exact and heuristic approaches to select a small subset of solutions that maximizes solution diversity. We obtain good results on binary variables, but report scaling problems when considering general integer and continuous variables.