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

In this paper we address the problem of drawing planar graphs with circular arcs while maintaining good angular resolution and small drawing area. We present a lower bound on the area of drawings in which edges are drawn using exactly one circular arc. We also give an algorithm for drawing n-vertex planar graphs such that the edges are sequences of two continuous circular arcs. The algorithm runs in O(n) time and embeds the graph on the O(n) × O(n) grid, while maintaining ?(1/d(v)) angular resolution, where d(v) is the degree of vertex v. Since in this case we use circular arcs of infinite radius, this is also the first algorithm that simultaneously achieves good angular resolution, small area, and at most one bend per edge using straight-line segments. Finally, we show how to create drawings in which edges are smooth C1-continuous curves, represented by a sequence of at most three circular arcs.

/pdf/drawing-planar-graphs-with-circular-arcs-dmjifjcnlu.pdf

Drawing planar graphs with circular arcs

A Lombardi drawing of a graph is one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (equal angles between consecutive edges, as measured by the tangents to the circular arcs at the vertex). We describe two algorithms that create "Lombardi-style" drawings (which we also call near-Lombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a force-directed, spring-embedding approach, with one using forces at edge tangents to produce curved edges and the other using dummy vertices on edges for this purpose. As we show, these approaches produce near-Lombardi drawings, with one being slightly better at achieving near-perfect angular resolution and the other being slightly better at balancing edge placements.

/pdf/force-directed-lombardi-style-graph-drawing-36fuw2q9kh.pdf

Force-Directed lombardi-style graph drawing

We present efficient algorithms for solving polygonal-path approximation problems in three and higher dimensions. Given an n -vertex polygonal curve P in \R

 d
 , d \geq 3 , we approximate P by another poly- gonal curve P' of m ≤ n vertices in \R

 d
 such that the vertex sequence of P' is an ordered subsequence of the vertices of P . The goal is either to minimize the size m of P' for a given error tolerance \eps (called the min-\# problem), or to minimize the deviation error \eps between P and P' for a given size m of P' (called the min- \eps problem). Our techniques enable us to develop efficient near-quadratic-time algorithms in three dimensions and subcubic-time algorithms in four dimensions for solving the min-\# and min-\eps problems. We discuss extensions of our solutions to d -dimensional space, where d > 4 , and for the L

 1
 and L

 ∈
 
fty metrics.

/pdf/efficiently-approximating-polygonal-paths-in-three-and-3ouihjw4n4.pdf

Efficiently approximating polygonal paths in three and higher dimensions

Secure pairing of electronic devices is an important issue that must be addressed in many contexts. In the absence of prior security context, the need to involve the user in the pairing process is a prominent challenge. In this paper, we investigate the use of the audio channel for human-assisted device pairing. First we assume a common (insecure) wireless channel between devices. We then obviate the assumption of a pre-existing common channel with a single-channel device pairing approach only based on audio. Both approaches are applicable to a wide range of devices and place light burden on the user.

http://sprout.ics.uci.edu/pubs/audio-ijsn.pdf

Using audio in secure device pairing

In this paper we present an efficient method for interpolating a piecewise-linear surface between two parallel slices, each consisting of an arbitrary number of (possibly nested) polygons that define 'material' and 'nonmaterial' regions. This problem has applications to medical imaging, geographic information systems, etc. Our method is fully automatic and is guaranteed to produce non-self-intersecting surfaces in all cases regardless of the number of contours in each slice, their complexity and geometry, and the depth of their hierarchy of nesting. The method is based on computing cells in the overlay of the slices, that form the symmetric difference between them. Then, the straight skeletons of the selected cells guide the triangulation of these cells. Finally, the resulting triangles are lifted up in space to form an interpolating surface. We provide some experimental results on various complex examples to show the good and robust performance of our algorithm.

/pdf/straight-skeleton-based-contour-interpolation-2b7hcs20ft.pdf

Michael T. Goodrich

Papers

Drawing planar graphs with circular arcs

Force-Directed lombardi-style graph drawing

Efficiently approximating polygonal paths in three and higher dimensions

Using audio in secure device pairing

Straight-skeleton based contour interpolation