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

Parallel prefix computation is perhaps the most frequently used subroutine in parallel algorithms today. Its time complexity on the CRCW PRAM is O(lg n/ lg lg n) using a polynomial number of processors, even in a randomized setting. Nevertheless, there are a number of non-trivial applications that have been shown to be solvable using only an approximate version of the prefix sums problem. In this paper we resolve the issue of approximating parallel prefix by introducing an algorithm that runs in O(lg* n) time with very high probability, using n/ lg’ n processors, which is optimal in terms of both work and running time. Our approximate prefix sums are guaranteed to come within a factor of (1 + E) of the values of the true sums in a “consistent fashion”, where E is o(1). We achieve this result through the use of a number of interesting new techniques, such as overcertification and estimate-focusing, as well as through new adaptations of known techniques, such as failure-sweeping and bit-thinning. We give a number of non-trivial applications of our approximate parallel prefix routine. Perhaps the most interesting application is for padded integer sorting, an approximation version of another fundamental problem in parallel algorithm design-integer sorting-where one wishes to sort R integers into an array of size 0(n), allowing for gaps between consecutive elements. We show that this problem can also be solved in O(lg’ n) time, with very high probability, using a linear amount of work, which is also optimal in both time and work. Finally, we show several applications ‘Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218. Email: goodrich& . jhu. edu. This research supported by the NSF and DARPA under Grant CCR8908092, and by the NSF under Grants IRI-9116843 and CCR-

Optimal parallel approximation for prefix sums and integer sorting

Given an off-line sequence S of n set-manipulation operations, we investigate the parallel complexity of evaluating S (i.e., finding the response to every operation in S and returning the resulting set). We show that the problem of evaluating S is in NC for various combinations of common set-manipulation operations. Once we establish membership in NC (or, if membership in NC is obvious), we develop techniques for improving the time and/or processor complexity.

/pdf/parallel-algorithms-for-evaluating-sequences-of-set-3497nyy1os.pdf

Parallel algorithms for evaluating sequences of set-manipulation operations

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. >

Sorting on a parallel pointer machine with applications to set expression evaluation

In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer’s mental map. The overall running time of the algorithm is O(n log n), where n is the number of vertices of graph G.

/pdf/planarity-preserving-clustering-and-embedding-for-large-4duntmcad1.pdf

Planarity-Preserving Clustering and Embedding for Large Planar Graphs

If you are the type that always orders vanilla in the ice cream shop, then you should probably sta y away from parallel algorithm design, for you may never get past the fact that any given paralle l algorithm may be designed for any one of several different computational models . If, on the other hand, you are the type who thinks there are still not enough channels on cable TV, then you migh t think the number of parallel models is woefully small . If you fall into neither camp, which, accordin g to the Chernoff bounds [22], you probably should, then you may find this first SIGACT News column on parallel algorithm design of some use . For here I review a \"classic\" model for parallel computatio n and I survey some interesting work on alternative models for parallel computation .

Michael T. Goodrich

Papers

Optimal parallel approximation for prefix sums and integer sorting

Parallel algorithms for evaluating sequences of set-manipulation operations

Sorting on a parallel pointer machine with applications to set expression evaluation

Planarity-Preserving Clustering and Embedding for Large Planar Graphs

Parallel algorithms column 1: models of computation