Michael T. Goodrich

Bio: Michael T. Goodrich is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Planar graph & Parallel algorithm. The author has an hindex of 61, co-authored 430 publications receiving 14045 citations. Previous affiliations of Michael T. Goodrich include New York University & Technion – Israel Institute of Technology.

Linear-Time Triangulation of a Simple Polygon Made Easier Via Randomization

Abstract: We describe a randomized algorithm for computing the trapezoidal decomposition of a simple polygon. Its expected running time is linear in the size of the polygon. By a well-known and simple linear time reduction, this implies a linear time algorithm for triangulating a simple polygon. Our algorithm is considerably simpler than Chazelle's (1991) celebrated optimal deterministic algorithm and, hence, positively answers his question of whether a simpler randomized algorithm for the problem exists. The new algorithm can be viewed as a combination of Chazelle's algorithm and of non-optimal randomized algorithms due to Clarkson et al. (1991) and to Seidel (1991), with the essential innovation that sampling is performed on subchains of the initial polygonal chain, rather than on its edges. It is also essential, as in Chazelle's algorithm, to include a bottom-up preprocessing phase previous to the top-down construction phase.

Reliable Resource Searching in P2P Networks

Abstract: We study the problem of securely searching for resources in p2p networks where a constant fraction of the peers may act maliciously. We present two novel hashing-based schemes that can be employed to reliably support resource location and content retrieval queries, limiting the ability of adversarial nodes to carry out attacks. Our schemes achieve scalability and load balancing and have small authentication overhead. In particular, for a network with n peers, resources are securely located with O(log2 n) messages and content from a collection of m data items is securely retrieved with O(logn logm) messages.

An Efficient Dynamic and Distributed RSA Accumulator

Abstract: We show how to use the RSA one-way accumulator to realize an efficient and dynamic authenticated dictionary, where untrusted directories provide cryptographically verifiable answers to membership queries on a set maintained by a trusted source. Our accumulator-based scheme for authenticated dictionaries supports efficient incremental updates of the underlying set by insertions and deletions of elements. Also, the user can optimally verify in constant time the authenticity of the answer provided by a directory with a simple and practical algorithm. We have also implemented this scheme and we give empirical results that can be used to determine the best strategy for systems implementation with respect to resources that are available. This work has applications to certificate revocation in public key infrastructure and end-to-end integrity of data collections published by third parties on the Internet.

C-Planarity Testing of Embedded Clustered Graphs with Bounded Dual Carving-Width

Abstract: For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a region homeomorphic to a closed disk such that 1. the subgraph induced by each cluster is drawn in the interior of the corresponding disk, 2. each edge intersects any disk at most once, and 3. the nesting between clusters is reflected by the representation, i.e., child clusters are properly contained in their parent cluster. The computational complexity of this problem, whose study has been central to the theory of graph visualization since its introduction in 1995 [Qing-Wen Feng, Robert F. Cohen, and Peter Eades. Planarity for clustered graphs. ESA'95], has only been recently settled [Radoslav Fulek and Csaba D. Toth. Atomic Embeddability, Clustered Planarity, and Thickenability. To appear at SODA'20]. Before such a breakthrough, the complexity question was still unsolved even when the graph has a prescribed planar embedding, i.e, for embedded clustered graphs. We show that the C-Planarity Testing problem admits a single-exponential single-parameter FPT algorithm for embedded clustered graphs, when parameterized by the carving-width of the dual graph of the input. This is the first FPT algorithm for this long-standing open problem with respect to a single notable graph-width parameter. Moreover, in the general case, the polynomial dependency of our FPT algorithm is smaller than the one of the algorithm by Fulek and Toth. To further strengthen the relevance of this result, we show that the C-Planarity Testing problem retains its computational complexity when parameterized by several other graph-width parameters, which may potentially lead to faster algorithms.

Capturing Lombardi Flow in Orthogonal Drawings by Minimizing the Number of Segments.

Abstract: Inspired by the artwork of Mark Lombardi, we study the problem of constructing orthogonal drawings where a small number of horizontal and vertical line segments covers all vertices. We study two problems on orthogonal drawings of planar graphs, one that minimizes the total number of line segments and another that minimizes the number of line segments that cover all the vertices. We show that the first problem can be solved by a non-trivial modification of the flow-network orthogonal bend-minimization algorithm of Tamassia, resulting in a polynomial-time algorithm. We show that the second problem is NP-hard even for planar graphs with maximum degree 3. Given this result, we then address this second optimization problem for trees and series-parallel graphs with maximum degree 3. For both graph classes, we give polynomial-time algorithms for upward orthogonal drawings with the minimum number of segments covering the vertices.

I and i

Abstract: 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 …

Random graphs

Abstract: 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.

Planning Algorithms: Introductory Material

Abstract: 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.

Internet of Things: A Survey on Enabling Technologies, Protocols, and Applications

Abstract: 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.

An efficient k-means clustering algorithm: analysis and implementation

Abstract: 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.