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

This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data. Unlike previous approaches, our study is not based on the assumption that road networks are planar graphs. Indeed, based on the a number of experiments we have performed on the road networks of the 50 United States and District of Columbia, we provide strong empirical evidence that road networks are quite non-planar. Our approach therefore instead is directed at finding algorithmically-motivated properties of road networks as non-planar geometric graphs, focusing on alternative properties of road networks that can still lead to efficient algorithms for such problems as shortest paths and Voronoi diagrams. In particular, we study road networks as multiscale-dispersed graphs, which is a concept we formalize in terms of disk neighborhood systems. This approach allows us to develop fast algorithms for road networks without making any additional assumptions about the distribution of edge weights. In fact, our algorithms can allow for non-metric weights.

Studying (Non-Planar) Road Networks Through an Algorithmic Lens

We describe simplified analyses of well-known randomized algorithms for searching, sorting, and selection. The proofs we include are quite simple and can easily be made a part of a Freshman-Sophomore Introduction to Data Structures (CS2) course and a Junior-Senior level course on the design and analysis of data structures and algorithms (CS7/DS&A). We show that using randomization in data structures and algorithms is safe and can be used to significantly simplify efficient solutions to various computational problems.

Simplified Analyses of Randomized Algorithms for Searching, Sorting, and Selection

We demonstrate the functionality of a distributed system that supports the wide-scale deployment of an authenticated map. The system can be easily extended to support applications that use authenticated maps, including certificate revocation, document integrity, and digital rights management.

Distributed data authentication

Combinatorial Algorithms.- Efficient Implementation of the WARM-UP Algorithm for the Construction of Length-Restricted Prefix Codes.- Implementing Weighted b-Matching Algorithms: Insights from a Computational Study.- Designing Practical Efficient Algorithms for Symmetric Multiprocessors.- Circular Drawings of Biconnected Graphs.- Heuristics and Experimental Design for Bigraph Crossing Number Minimization.- Binary Space Parititions in Plucker Space.- Practical Point-in-Polygon Tests Using CSG Representations of Polygons.- Software and Applications.- Accessing the Internal Organization of Data Structures in the JDSL Library.- Object-Oriented Design of Graph Oriented Data Structures.- A Case Study on the Cost of Geometric Computing.- Design and Implementation of the Fiduccia-Mattheyses Heuristic for VLSI Netlist Partitioning.- Algorithms for Restoration Planning in a Telecommunications Network.- Computing the n x m Shortest Paths Efficiently.- Image Watermarking for Copyright Protection.- Algorithms for NP-Hard Problems.- A Self Organizing Bin Packing Heuristic.- Finding the Right Cutting Planes for the TSP.- Obstacle-Avoiding Euclidean Steiner Trees in the Plane: An Exact Algorithm.- Data Structures.- Adaptive Algorithms for Cache-efficient Trie Search.- Fast Priority Queues for Cached Memory.- Efficient Bulk Operations on Dynamic R-trees.

Algorithm Engineering and Experimentation: International Workshop ALENEX'99 Baltimore, MD, USA, January 15-16, 1999, Selected Papers

For a source node, v, and target node, w, the traceroute command iteratively issues “kth-hop” queries, for k = 1, 2, . . . , δ(v, w), which return the name of the kth vertex on a shortest path from v to w, where δ(v, w) is the distance between v and w, that is, the number of edges in a shortest-path from v to w. The traceroute command is often used for network mapping applications, the study of the connectivity of networks, and it has been studied theoretically with respect to biases it introduces for network mapping when only a subset of nodes in the network can be the source of traceroute queries. In this paper, we provide efficient network mapping algorithms, that are based on kth-hop traceroute queries. Our results include an algorithm that runs in a constant number of parallel rounds with a subquadratic number of queries under reasonable assumptions about the sampling coverage of the nodes that may issue kth-hop traceroute queries. In addition, we introduce a number of new algorithmic techniques, including a high-probability parametric parallelization of a graph clustering technique of Thorup and Zwick, which may be of independent interest. 2012 ACM Subject Classification Theory of computation → Parallel algorithms; Networks → Network algorithms; Mathematics of computing → Graph theory; Mathematics of computing → Probabilistic algorithms

Michael T. Goodrich

Papers

Studying (Non-Planar) Road Networks Through an Algorithmic Lens

Simplified Analyses of Randomized Algorithms for Searching, Sorting, and Selection

Distributed data authentication

Algorithm Engineering and Experimentation: International Workshop ALENEX'99 Baltimore, MD, USA, January 15-16, 1999, Selected Papers

Mapping Networks via Parallel kth-Hop Traceroute Queries