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.

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An efficient k-means clustering algorithm: analysis and implementation

We describe algorithms for canonically partitioning semi-regular quadrilateral meshes into structured submeshes, using an adaptation of the geometric motorcycle graph of Eppstein and Erickson to quad meshes. Our partitions may be used to efficiently find isomorphisms between quad meshes. In addition, they may be used as a highly compressed representation of the original mesh. These partitions can be constructed in sublinear time from a list of the extraordinary vertices in a mesh. We also study the problem of further reducing the number of submeshes in our partitions---we prove that optimizing this number is NP-hard, but it can be efficiently approximated.

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Motorcycle graphs: canonical quad mesh partitioning

* Presents a consistent object-oriented perspective* Recursion emphasized throughout, particularly in chapters 2 and 4* Design patterns provide clear approaches for developing programs* Offers a unique multimedia format for learning the fundamentals of data structures and algorithms* A robust set of end-of-chapter problems are arranged by purpose - reinforcement problems assess understanding; creativity problems require students to apply concepts to writing "classes" (portions of a program); projects require students to write entire programs* Outstanding writing style presents even the most difficult mathematical concepts clearly* "Visual Proofs" helps students better understand complex analytic concepts* Animations on the text's Web site clearly illustrate data structures and algorithms* Exercises offer numerous opportunities for hands-on learning* Emphasizes the practical application of the latest software engineering practices

Data structures and algorithms in C

We present techniques which result in improved parallel algorithms for a number of problems whose efficient sequential algorithms use the plane-sweeping paradigm. The problems for which we give improved algorithms include intersection detection, trapezoidal decomposition, triangulation, and planar point location. Our technique can be used to improve on the previous time bound while keeping the space and processor bounds the same, or improve on the previous space bound while keeping the time and processor bounds the same. We also give efficient parallel algorithms for visibility from a point, 3-dimensional maxima, multiple range-counting, and rectilinear segment intersection counting. We never use the AKS sorting network in any of our algorithms.

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Efficient plane sweeping in parallel

We show that greedy geometric routing schemes exist for the Euclidean metric in R 2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(logn) bits, where n is the number of vertices in the graph.

Succinct Greedy Geometric Routing in the Euclidean Plane

Introducing a NEW addition to our growing library of computer science titles,Algorithm Design and Applications, by Michael T. Goodrich & Roberto Tamassia! Algorithms is a course required for all computer science majors, with a strong focus on theoretical topics. Students enter the course after gaining hands-on experience with computers, and are expected to learn how algorithms can be applied to a variety of contexts. This new book integrates application with theory. Goodrich & Tamassia believe that the best way to teach algorithmic topics is to present them in a context that is motivated from applications to uses in society, computer games, computing industry, science, engineering, and the internet. The text teaches students about designing and using algorithms, illustrating connections between topics being taught and their potential applications, increasing engagement.

Michael T. Goodrich

Papers

Motorcycle graphs: canonical quad mesh partitioning

Data structures and algorithms in C

Efficient plane sweeping in parallel

Succinct Greedy Geometric Routing in the Euclidean Plane

Algorithm Design and Applications