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.

Approximate topological matching of quadrilateral meshes

Abstract: We study approximate topological matching of quadrilateral meshes, that is, the problem of finding as large a set as possible of matching portions of two quadrilateral meshes. This study is motivated by applications in graphics that involve shape modeling whose results need to be merged in order to produce a final unified representation of an object. We show that the problem of producing a maximum approximate topological match of two quad meshes in NP-hard. Given this result, which makes an exact solution extremely unlikely, we show that the natural greedy algorithm derived from polynomial-time graph isomorphism can produce poor results, even when it is possible to find matches with only a few non-matching quads. Nevertheless, we provide a "lazy-greedy" algorithm that is guaranteed to find good matches when mis-matching portions of mesh are localized. Finally, we provide empirical evidence that this approach produces good matches between similar quad meshes.

Tracking Paths in Planar Graphs

Abstract: We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et. al. [3]. Given an undirected graph with a source $s$ and a destination $t$, find the smallest subset of vertices whose intersection with any $s-t$ path results in a unique sequence. In this paper, we show that this problem remains NP-complete when the graph is planar and we give a 4-approximation algorithm in this setting. We also show, via Courcelle's theorem, that it can be solved in linear time for graphs of bounded-clique width, when its clique decomposition is given in advance.

Round-trip voronoi diagrams and doubling density in geographic networks

Abstract: Given a geographic network G (e.g. road network, utility distribution grid) and a set of sites (e.g. post offices, fire stations), a two-site Voronoi diagram labels each vertex v∈G with the pair of sites that minimizes some distance function. The sum function defines the “distance” from v to a pair of sites s,t as the sum of the distances from v to each site. The round-trip function defines the “distance” as the minimum length tour starting and ending at v and visiting both s and t. A two-color variant begins with two different types of sites and labels each vertex with the minimum pair of sites of different types. In this paper, we provide new properties and algorithms for two-site and two-color Voronoi diagrams for these distance functions in a geographic network, including experimental results on the doubling distance of various point-of-interest sites. We extend some of these results to multi-color variants.

Succinct Greedy Geometric Routing in the Euclidean Plane

Abstract: 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. We show that greedy geometric routing schemes exist for the Euclidean metric in R^2, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits, where n is the number of vertices in the graph. Moreover, our embedding strategy introduces a coordinate system for R^2 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^2.

Parallel external memory model - a parallel model for multi-core architectures

Abstract: In this dissertation we propose the parallel external memory (PEM) model – a parallel model for private-cache chip multiprocessors (CMPs). By focusing on private-cache CMPs, we show that we can design efficient algorithms that need no additional assumptions about the way that processors are interconnected. In particular we assume that all inter-processor communication occurs through the memory hierarchy. We study several parallel algorithms fundamental for any parallel model: all-prefix-sums, gather and scatter, selection, partitioning and sorting. We also study problems on graphs. We present efficient solution to the list ranking problem – a key result to solving other problems on graphs in parallel. We address the problems of finding Euler tour and lowest common ancestors on trees, connected and bi-connected components on graphs, minimum spanning tree on connected graphs and ear decomposition on bi-connected graphs. Finally, we address the computational geometry problem of computing the convex hull on a set of points in the plane.

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.