Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Active Learning to Maximize Area Under the ROC Curve

In active learning, a machine learning algorithmis given an unlabeled set of examples U, and is allowed to request labels for a relatively small subset of U to use for training. The goal is then to judiciously choose which examples in U to have labeled in order to optimize some performance criterion, e.g. classification accuracy. We study how active learning affects AUC. We examine two existing algorithms from the literature and present our own active learning algorithms designed to maximize the AUC of the hypothesis. One of our algorithms was consistently the top performer, and Closest Sampling from the literature often came in second behind it. When good posterior probability estimates were available, our heuristics were by far the best.

Bandit-Based Algorithms for Budgeted Learning

We explore the problem of budgeted machine learning, in which the learning algorithm has free access to the training examples’ labels but has to pay for each attribute that is specified. This learning model is appropriate in many areas, including medical applications. We present new algorithms for choosing which attributes to purchase of which examples in the budgeted learning model based on algorithms for the multi-armed bandit problem. All of our approaches outperformed the current state of the art. Furthermore, we present a new means for selecting an example to purchase after the attribute is selected, instead of selecting an example uniformly at random, which is typically done. Our new example selection method improved performance of all the algorithms we tested, both ours and those in the literature.