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 present the software architecture and implementation of an eficient data structure for dynamically maintaining an authenticated dictionary. The building blocks of the data structure are skip lists and one-way commutative hash functions. We also present the results of a preliminary experiment on the performance of the data structure. Applications of our work include certijicate revocation in public key infrastructure and the pubkcation of data collections on the Internet.

Implementation of an Authenticated Dictionary

We study the parallel query complexity of reconstructing binary trees from simple queries involving their nodes. We show that a querier can efficiently reconstruct a binary tree with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries.

https://dl.acm.org/doi/pdf/10.1145/3350755.3400229

Reconstructing Binary Trees in Parallel

We characterize four classes of geometric membership and containment orders-structurally and in terms of forbidden subposets-and present linear- or near linear-time recognition algorithms for each class. We also show that recognizing point-halfspace orders in ℝ2 is NP-hard for d≥2.

/pdf/characterization-and-recognition-of-point-halfspace-and-595emyrf7g.pdf

Characterization and Recognition of Point-Halfspace and Related Orders

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an \(n\times n\) grid of pixels with k centers, the problem can be solved in time \(O(n^2 \log ^5 n)\), and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a k-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable k-means in order to improve the connectivity of the resulting clusters.

/pdf/algorithms-for-stable-matching-and-clustering-in-a-grid-1hdbayo1wc.pdf

Algorithms for Stable Matching and Clustering in a Grid

In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. In this paper, we study greedy geometric routing in R, using the standard Euclidean metric. Greedy geometric routing is not always possible in fixed-dimensional Euclidean spaces, of course, as is the case, for example, with star graphs. Nevertheless, we show that such greedy geometric routing schemes exist in R, for 3-connected planar graphs, using the standard Euclidean metric, with coordinates that can be represented succinctly, that is, with O(log n) bits. Moreover, our embedding strategy introduces a coordinate system for R that supports distance comparisons using our succinct coordinates. Thus, our scheme can be used to significantly reduce bandwidth, space, and header size over other recently discovered greedy geometric routing implementations for R. ar X iv :0 81 2. 38 93 v1 [ cs .C G ] 1 9 D ec 2 00 8

Michael T. Goodrich

Papers

Implementation of an Authenticated Dictionary

Reconstructing Binary Trees in Parallel

Characterization and Recognition of Point-Halfspace and Related Orders

Algorithms for Stable Matching and Clustering in a Grid

Succinct Greedy Geometric Routing in R^2