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We have created a large diverse set of cars from overhead images, which are useful for training a deep learner to binary classify, detect and count them. The dataset and all related material will be made publically available. The set contains contextual matter to aid in identification of difficult targets. We demonstrate classification and detection on this dataset using a neural network we call ResCeption. This network combines residual learning with Inception-style layers and is used to count cars in one look. This is a new way to count objects rather than by localization or density estimation. It is fairly accurate, fast and easy to implement. Additionally, the counting method is not car or scene specific. It would be easy to train this method to count other kinds of objects and counting over new scenes requires no extra set up or assumptions about object locations., ECCV 2016 Pre-press revision

Folding an n ×n checkerboard pattern from a square of paper that is white on one side and black on the other has been thought for several years to require a paper square of semiperimeter n 2 [superscript 2]. Indeed, within a restricted class of foldings that match all previous origami models of this flavor, one can prove a lower bound of n 2 [superscript 2](though a matching upper bound was not known). We show how to break through this barrier and fold an n ×n checkerboard from a paper square of semiperimeter 1/2 n2 [superscript 2] + O(n) In particular, our construction strictly beats semiperimeter n 2 [superscript 2] for (even) n > 16, and for n = 8, we improve on the best seamless folding., National Science Foundation (U.S.) (CAREER award CCF-0347776)

Given a weighted graph with some subsets of vertices called groups, the group Steiner tree problem is to find a minimum-weight subgraph which contains at least one vertex from each group. We give a randomized algorithm with a polylogarithmic approximation guarantee for the group Steiner tree problem. The previous best approximation guarantee was O(i2k1/i) in time O(nik2i) (Charikar, Chekuri, Goel, and Guha). Our algorithm also improves existing approximation results for network design problems with location-based constraints and for the symmetric generalized traveling salesman problem.

Networks are a mathematical abstraction of the interactions between a set of entities, with extensive applications in social science, epidemiology, bioinformatics, and cybersecurity, among others. There are many fundamental problems when analyzing network data, such as anomaly detection, dense subgraph mining, motif finding, information diffusion, and epidemic spread. A common underlying task in all these problems is finding an "interesting subgraph"; that is, finding a part of the graph---usually small relative to the whole---that optimizes a score function and has some property of interest, such as connectivity or a minimum density. Finding subgraphs that satisfy common constraints of interest, such as the ones above, is computationally hard in general, and state-of-the-art algorithms for many problems in network analysis are heuristic in nature. These methods are fast and usually easy to implement. However, they come with no theoretical guarantees on the quality of the solution, which makes it difficult to assess how the discovered subgraphs compare to an optimal solution, which in turn affects the data mining task at hand. For instance, in anomaly detection, solutions with low anomaly score lead to sub-optimal detection power. On the other end of the spectrum, there have been significant advances on approximation algorithms for these challenging graph problems in the theoretical computer science community. However, these algorithms tend to be slow, difficult to implement, and they do not scale to the large datasets that are common nowadays. The goal of this dissertation is developing scalable algorithms with theoretical guarantees for various network analysis problems, where the underlying task is to find subgraphs with constraints. We find interesting subgraphs with guarantees by adapting techniques from parameterized complexity, convex optimization, and submodularity optimization. These techniques are well-known in the algorithm design literature, but they lead to slow and impractical algorithms. One unifying theme in the problems that we study is that our methods are scalable without sacrificing the theoretical guarantees of these algorithm design techniques. We accomplish this combination of scalability and rigorous bounds by exploiting properties of the problems we are trying to optimize, decomposing or compressing the input graph to a manageable size, and parallelization. We consider problems on network analysis for both static and dynamic network models. And we illustrate the power of our methods in applications, such as public health, sensor data analysis, and event detection using social media data. Ph. D.