There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

This paper provides an overview of the Internet of Things (IoT) with emphasis on enabling technologies, protocols, and application issues. The IoT is enabled by the latest developments in RFID, smart sensors, communication technologies, and Internet protocols. The basic premise is to have smart sensors collaborate directly without human involvement to deliver a new class of applications. The current revolution in Internet, mobile, and machine-to-machine (M2M) technologies can be seen as the first phase of the IoT. In the coming years, the IoT is expected to bridge diverse technologies to enable new applications by connecting physical objects together in support of intelligent decision making. This paper starts by providing a horizontal overview of the IoT. Then, we give an overview of some technical details that pertain to the IoT enabling technologies, protocols, and applications. Compared to other survey papers in the field, our objective is to provide a more thorough summary of the most relevant protocols and application issues to enable researchers and application developers to get up to speed quickly on how the different protocols fit together to deliver desired functionalities without having to go through RFCs and the standards specifications. We also provide an overview of some of the key IoT challenges presented in the recent literature and provide a summary of related research work. Moreover, we explore the relation between the IoT and other emerging technologies including big data analytics and cloud and fog computing. We also present the need for better horizontal integration among IoT services. Finally, we present detailed service use-cases to illustrate how the different protocols presented in the paper fit together to deliver desired IoT services.

Internet of Things: A Survey on Enabling Technologies, Protocols, and Applications

In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.

/pdf/an-efficient-k-means-clustering-algorithm-analysis-and-1vgn3zr7cg.pdf

An efficient k-means clustering algorithm: analysis and implementation

We study the online problem of assigning a moving point to a base-station region that contains it. Our goal is to minimize the number of handovers that occur when the point moves outside its assigned region and must be assigned to a new one. We study this problem in terms of a competitive analysis measured as a function of Δ, the ply of the system of regions, that is, the maximum number of regions that cover any single point.

Tracking moving objects with few handovers

In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder, Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier, Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries and path queries Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study Moreover, through an experimental analysis using both real-world and synthetic data, we provide empirical evidence that our algorithms provide significant parallel speedups while also improving the total query complexities for the problems we study

Reconstructing Biological and Digital Phylogenetic Trees in Parallel

An algorithm for the well-known hidden-surface elimination problem for rectangles, which is also known as the window rendering problem is presented. The time complexity of the algorithm is sensitive to the size of the output. Specifically, it runs in time that is O (n(1.5) + k), where k is the size of the output (which can be as large as theta (n(squared)). For values of k in the range between n(1.5)/log n and n squared, the algorithm is asymptotically faster than previous ones.

/pdf/output-sensitive-hidden-surface-elimination-for-rectangles-3w6vge3xgk.pdf

Output-Sensitive Hidden Surface Elimination for Rectangles

The exemplary embodiments of this invention provides notarized federated identity management that may have application like supporting efficient user authentication when providers are unknown to each other and/or for avoiding direct communication between identity providers and service providers, which provides improved privacy protection for users. In one non-limiting, exemplary embodiment, a method includes: receiving through a data communication network an assertion generated by a first entity; notarizing the assertion to obtain a corresponding notarized assertion; and in response to receiving from a second entity via the same or a different data communication; network a query corresponding to the assertion, returning the corresponding notarized assertion. The method further includes: determining a user private key for the user identity information; and returning the user private key to the user as data to be stored on a storage medium.

Notarized federated identity management

We show that finding a minimum-width orthogonal upward drawing of a phylogenetic tree is NP-hard for binary trees with unconstrained combinatorial order and provide a linear-time algorithm for ordered trees. We also study several heuristic algorithms for the unconstrained case and show their effectiveness through experimentation.

Michael T. Goodrich

Papers

Tracking moving objects with few handovers

Reconstructing Biological and Digital Phylogenetic Trees in Parallel

Output-Sensitive Hidden Surface Elimination for Rectangles

Notarized federated identity management

Minimum-Width Drawings of Phylogenetic Trees