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

The completeness of road network data is significant in the quality of various routing services and applications. We introduce an efficient randomized algorithm for exact learning of road networks using simple distance queries, which can find missing roads and improve the quality of routing services. The efficiency of our algorithm depends on a cluster degree parameter, d max , which is an upper bound on the degrees of vertex clusters defined during our algorithm. Unfortunately, we leave open the problem of theoretically bounding d max , although we conjecture that d max is small for road networks and other similar types of graphs. We support this conjecture by experimentally evaluating our algorithm on road network data for the U.S. and 5 European countries of various sizes. This analysis provides experimental evidence that our algorithm issues a quasilinear number of queries in expectation for road networks and similar graphs. of → Graph analysis; Theory of → Random network models;

Efficient Exact Learning Algorithms for Road Networks and Other Graphs with Bounded Clustering Degrees

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface $\cal S$ of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema $\cal P$ for $\cal S$. Our drawings are planar, but they allow for multiple copies of vertices and edges on $\cal P$'s boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.

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Planar drawings of higher-genus graphs

Data Structures in JDSL

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Classic-Style뀀ȠSeries-Parallel뀀ȠDrawings Single-Row뀀ȠTheorems/Figures뀀Ƞ Fixed-Width뀀ȠTheorems/Figures Experiments

We introduce the problem of performing set-difference range queries, where answers to queries are set-theoretic symmetric differences between sets of items in two geometric ranges. We describe a general framework for answering such queries based on a novel use of data-streaming sketches we call signed symmetric-difference sketches. We show that such sketches can be realized using invertible Bloom filters (IBFs), which can be composed, differenced, and searched so as to solve set-difference range queries in a wide range of scenarios. ∗Dept. of Comp. Sci., U. of CA, Irvine, eppstein(at)uci.edu †Dept. of Comp. Sci., U. of CA, Irvine, goodrich(at)uci.edu ‡Dept. of Comp. Sci., U. of CA, Irvine, jsimons(at)uci.edu 0 ar X iv :1 30 6. 34 82 v1 [ cs .D S] 1 4 Ju n 20 13 (a) (b) Figure 1: Illustrating the set-difference range query problem. The images in (a) and (b) have four major differences, three of which are inside the common query range. The image (a) is a public-domain engraving of an astronomer by Albrecht Durer, from the title page of Messahalah, De scientia motus orbis (1504).

Michael T. Goodrich

Papers

Efficient Exact Learning Algorithms for Road Networks and Other Graphs with Bounded Clustering Degrees

Planar drawings of higher-genus graphs

Data Structures in JDSL

Classic-Style뀀ȠSeries-Parallel뀀ȠDrawings Single-Row뀀ȠTheorems/Figures뀀Ƞ Fixed-Width뀀ȠTheorems/Figures Experiments

Set-Difference Range Queries