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

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph's vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem.

Choosing Colors for Geometric Graphs via Color Space Embeddings

In this paper, we study sparsity-exploiting Mastermind algorithms for attacking the privacy of an entire database of character strings or vectors, such as DNA strings, movie ratings, or social network friendship data. Based on reductions to nonadaptive group testing, our methods are able to take advantage of minimal amounts of privacy leakage, such as contained in a single bit that indicates if two people in a medical database have any common genetic mutations, or if two people have any common friends in an online social network. We analyze our Mastermind attack algorithms using theoretical characterizations that provide sublinear bounds on the number of queries needed to clone the database, as well as experimental tests on genomic information, collaborative filtering data, and online social networks. By taking advantage of the generally sparse nature of these real-world databases and modulating a parameter that controls query sparsity, we demonstrate that relatively few nonadaptive queries are needed to recover a large majority of each database.

Nonadaptive Mastermind Algorithms for String and Vector Databases, with Case Studies

We provide linear-time algorithms for geometric graphs with sublinearly many edge crossings. That is, we provide algorithms running in $O(n)$ time on connected geometric graphs having $n$ vertices and $k$ pairwise crossings, where $k$ is smaller than $n$ by an iterated logarithmic factor. Specific problems that we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no assumptions about the distribution or bit complexities of edge weights, nor do we utilize unusual bit-level operations on memory words. Instead, our algorithms are based on a planarization method that “zeros in” on edge crossings, together with methods for applying planar separator decompositions to geometric graphs with sublinearly many crossings. Incidentally, our planarization algorithm also solves an open computational geometry problem of Chazelle for triangulating a self-intersecting polygonal chain having $n$ segments and $k$ crossings in linear time, for the case when $k$ is sublinear in $n$ by an iterated logarithmic factor.

Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

This paper presents an approach to IP traceback based on the probabilistic packet marking paradigm. Our ap- proach, which we call randomize-and-link, uses large checksum cords to "link" message fragments in a way that is highly scalable, for the checksums serve both as associative addresses and data integrity verifiers. The main advantage of these checksum cords is that they spread the addresses of possible router messages across a spectrum that is too large for the attacker to easily create messages that collide with legitimate messages. Index Terms—Associate addresses, checksum cords, distributed denial of service (DDOS), IP, probabilistic packet marking, trace- back.

Probabilistic Packet Marking for Large-Scale

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2π/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area.

Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.

/pdf/drawing-trees-with-perfect-angular-resolution-and-polynomial-2rt5u1hul3.pdf

Michael T. Goodrich

Papers

Choosing Colors for Geometric Graphs via Color Space Embeddings

Nonadaptive Mastermind Algorithms for String and Vector Databases, with Case Studies

Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

Probabilistic Packet Marking for Large-Scale

Drawing trees with perfect angular resolution and polynomial area