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 present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries.

The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

We study parallel algorithms for identifying the dead sensors in a mobile ad hoc wireless network and for resolving broadcast conflicts on a multiple access channel (MAC). Our approach involves the development and application of new group-testing algorithms, where we are asked to identify all the defective items in a set of items when we can test arbitrary subsets of items. In the standard group-testing problem, the result of a test is binary--the tested subset either contains defective items or not. In the versions we study in this paper, the result of each test is non-binary. For example, it may indicate whether the number of defective items contained in the tested subset is zero, one, or at least two (i.e., the results are 0, 1, or 2+). We give adaptive algorithms that are provably more efficient than previous group testing algorithms (even for generalized response models). We also show how our algorithms can be implemented in parallel, because they possess a property we call conciseness, which allows them to be used to solve dead sensor diagnosis and conflict resolution on a MAC. Dead sensor diagnosis poses an interesting challenge compared to MAC resolution, because dead sensors are not locally detectable, nor are they themselves active participants. Even so, we present algorithms that can be applied in both contexts that are more efficient than previous methods. We also give lower bounds for generalized group testing.

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Efficient parallel algorithms for dead sensor diagnosis and multiple access channels

In the Constructive Solid Geometry (CSG) representation a geometric solid is represented as the hierarchical combination of a number of primitive shapes using boolean operations, such as and, or, minus, and xor. We study the sequential Oimecomplexity of solving various classification problems for CSG representations. Specifically, we address the problems of determining the boundary of a CSG representation (CSG evaluation) and determining all intersections of a Iine with a CSG model (line classification). These problems have applications to VLSI design, computer graphics, and solid modeling. Our algorithms improve the previous worstcase bounds for solving these problems, and are based on the paradigm of applying techniques from parallel processing theory to quickly perform the classifications sequent.idly. Moreover, since the operations in our algorithms can be implemented using simple procedures, such as graph/tree traversal: plane-sweeping, and table look-up, our methods should also be competitive in practice.

Applying parallel processing techniques to classification problems in constructive solid geometry

In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include:General hidden-surface elimination (even if the overlap relation contains cycles).CSG boundary evaluation.Computing the contour of a collection of rectangles.Hidden-surface elimination for rectangles.

There are interesting subproblems that we solve as a part of each parallelization. For example, we give an optimal parallel method for building a data structure for line-stabbing queries (which, incidentally, improves the sequential complexity of this problem). Our algorithms are for the CREW PRAM, unless otherwise noted.

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Sweep methods for parallel computational geometry

Optimal algorithms for sorting on parallel CREW (concurrent read, exclusive write) and EREW (exclusive read, exclusive write) versions of the pointer machine model are presented. Intuitively, these methods can be viewed as being based on the use of linked lists rather than arrays (the usual parallel data structure). It is shown how to exploit the 'locality' of the approach to solve a problem with applications to database querying and logic programming (set-expression evaluation) in O(log n) time using O(n) processors.<<ETX>>

Michael T. Goodrich

Papers

The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

Efficient parallel algorithms for dead sensor diagnosis and multiple access channels

Applying parallel processing techniques to classification problems in constructive solid geometry

Sweep methods for parallel computational geometry

Sorting on a Parallel Pointer Machine with Applications to Set Expression Evaluation (Preliminary Version)