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 address the problem of replicating a Voronoi diagram V(S) of a planar point set S by making proximity queries: 1. the exact location of the nearest site(s) in S 2. the distance to and label(s) of the nearest site(s) in S 3. a unique label for every nearest site in S.

In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.

Cloning Voronoi diagrams via retroactive data structures

We present a distributed data structure, which we call the rainbow skip graph. To our knowledge, this is the first peer-to-peer data structure that simultaneously achieves high fault tolerance, constant-sized nodes, and fast update and query times for ordered data. It is a non-trivial adaptation of the SkipNet/skip-graph structures of Harvey et al. and Aspnes and Shah, so as to provide fault-tolerance as these structures do, but to do so using constant-sized nodes, as in the family tree structure of Zatloukal and Harvey. It supports successor queries on a set of n items using O(log n) messages with high probability, an improvement over the expected O(log n) messages of the family tree.

The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree P2P Relay Structure

In this paper we give an optimal algorithm for constructing the convex hull of a partially sorted set S of n points in R 2 . Specifically, we assume S is represented as the union of a collection of non-empty subsets S 0 , S 1 , S 2 ,…, S m , where the x -coordinate of each point in S i is smaller than the x -coordinate of any point in S j if i j . Our method runs in O( n log h max ) time, where h max is the maximum number of hull edges incident on the points of any single subset S i . In fact, if one is only interested in finding the hull edges that ‘bridge’ different subsets, then our method runs in O( n ) time.

Constructing the convex hull of a partially sorted set of points

In the Constructive Solid Geometry (CSG) representation a geometric object is described as the hierarchical combination of a number of primitive shapes using the operations union, intersection, subtraction, and exclusive-union. This hierarchical description defines an expression tree, T, called the CSG tree, with leaves associated with primitive shapes, internal nodes associated with operations, and whose "value" is the geometric object. Evaluation of CSG trees is an important computation that arises in many rendering and analysis problems for geometric models, with ray shooting (also known as "ray casting") being one of the most important. Given any CSG tree T, which may be unbalanced, we show how to convert T into a functionally-equivalent binary tree, D, that is balanced. We demonstrate the utility of this conversion by showing how it can be used to improve the worst-case running time for ray shooting against a CSG model from O(n2) to O(n log n), which is optimal. In addition, the practicality of our method has been demonstrated in experimental benchmarking tests using the BRL-CAD package.

An Improved Ray Shooting Method for Constructive Solid Geometry Models Via Tree Contraction

We study the problem of abstracting a table of data about individuals so that no selection query can identify fewer than k individuals. We show that it is impossible to achieve arbitrarily good polynomial-time approximations for a number of natural variations of the generalization technique, unless P = NP , even when the table has only a single quasi-identifying attribute that represents a geographic or unordered attribute:


- Zip-codes : nodes of a planar graph generalized into connected subgraphs
- GPS coordinates : points in R2 generalized into non-overlapping rectangles
- Unordered data : text labels that can be grouped arbitrarily.



These hard single-attribute instances of generalization problems contrast with the previously known NP-hard instances, which require the number of attributes to be proportional to the number of individual records (the rows of the table). In addition to impossibility results, we provide approximation algorithms for these difficult single-attribute generalization problems, which, of course, apply to multiple-attribute instances with one that is quasi-identifying. Incidentally, the generalization problem for unordered data can be viewed as a novel type of bin packing problem---min-max bin covering ---which may be of independent interest.

Michael T. Goodrich

Papers

Cloning Voronoi diagrams via retroactive data structures

The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree P2P Relay Structure

Constructing the convex hull of a partially sorted set of points

An Improved Ray Shooting Method for Constructive Solid Geometry Models Via Tree Contraction

On the Approximability of Geometric and Geographic Generalization and the Min-Max Bin Covering Problem