arXiv subjects

Michael T. Goodrich

Publications and source records attributed to Michael T. Goodrich.

125 records · Page 7Linked to original sources

arXiv2009

The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree P2P Relay Structure

We present a distributed data structure, which we call the rainbow skip graph. To our knowledge, this is the first peer-to-peer data structure that simultaneously achieves high fault tolerance, constant-sized nodes, and fast update and query times for ordered data. It is a non-trivial adaptation of the SkipNet/skip-graph structures of Harvey et al. and Aspnes and Shah, so as to provide fault-tolerance as these structures do, but to do so using constant-sized nodes, as in the family tree structure of Zatloukal and Harvey. It supports successor queries on a set of n items using O(log n) messages with high probability, an improvement over the expected O(log n) messages of the family tree.

cs.DS↗

arXiv2009

On the Approximability of Geometric and Geographic Generalization and the Min-Max Bin Covering Problem

We study the problem of abstracting a table of data about individuals so that no selection query can identify fewer than k individuals. We show that it is impossible to achieve arbitrarily good polynomial-time approximations for a number of natural variations of the generalization technique, unless P = NP, even when the table has only a single quasi-identifying attribute that represents a geographic or unordered attribute: Zip-codes: nodes of a planar graph generalized into connected subgraphs GPS coordinates: points in R2 generalized into non-overlapping rectangles Unordered data: text labels that can be grouped arbitrarily. In addition to impossibility results, we provide approximation algorithms for these difficult single-attribute generalization problems, which, of course, apply to multiple-attribute instances with one that is quasi-identifying. We show theoretically and experimentally that our approximation algorithms can come reasonably close to optimal solutions. Incidentally, the generalization problem for unordered data can be viewed as a novel type of bin packing problem--min-max bin covering--which may be of independent interest.

cs.DS↗

arXiv2009

Improved Adaptive Group Testing Algorithms with Applications to Multiple Access Channels and Dead Sensor Diagnosis

We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the defective items in a set of items when we can test arbitrary subsets of items. In the standard group-testing problem, the result of a test is binary--the tested subset either contains defective items or not. In the more generalized versions we study in this paper, the result of each test is non-binary. For example, it may indicate whether the number of defective items contained in the tested subset is zero, one, or at least two. We give adaptive algorithms that are provably more efficient than previous group testing algorithms. We also show how our algorithms can be applied to solve conflict resolution on a MAC and dead sensor diagnosis. Dead sensor diagnosis poses an interesting challenge compared to MAC resolution, because dead sensors are not locally detectable, nor are they themselves active participants.

cs.DS↗

arXiv2009

An Efficient Dynamic and Distributed RSA Accumulator

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.

cs.CR↗

arXiv2009

On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results

In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms for discovering a hidden vector through single-color queries. Indeed, our algorithm improves a previous method of Chvatal by almost a factor of 2.

cs.DS↗

arXiv2009

Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric

This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric.

cs.DS↗

arXiv2008

Succinct Greedy Graph Drawing in the Hyperbolic Plane

We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that receives M pass it along to any neighbor that is closer in the hyperbolic metric to the message's eventual destination. More importantly, for networking applications, our algorithm produces succinct drawings, in that each of the vertex positions in one of our embeddings can be represented using O(log n) bits and the calculation of which neighbor to send a message to may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited.

cs.CG↗

arXiv2008

Straight Skeletons of Three-Dimensional Polyhedra

This paper studies the straight skeleton of polyhedra in three dimensions. We first address voxel-based polyhedra (polycubes), formed as the union of a collection of cubical (axis-aligned) voxels. We analyze the ways in which the skeleton may intersect each voxel of the polyhedron, and show that the skeleton may be constructed by a simple voxel-sweeping algorithm taking constant time per voxel. In addition, we describe a more complex algorithm for straight skeletons of voxel-based polyhedra, which takes time proportional to the area of the surfaces of the straight skeleton rather than the volume of the polyhedron. We also consider more general polyhedra with axis-parallel edges and faces, and show that any n-vertex polyhedron of this type has a straight skeleton with O(n^2) features. We provide algorithms for constructing the straight skeleton, with running time O(min(n^2 log n, k log^{O(1)} n)) where k is the output complexity. Next, we discuss the straight skeleton of a general nonconvex polyhedron. We show that it has an ambiguity issue, and suggest a consistent method to resolve it. We prove that the straight skeleton of a general polyhedron has a superquadratic complexity in the worst case. Finally, we report on an implementation of a simple algorithm for the general case.

cs.CG↗

arXiv2006

Choosing Colors for Geometric Graphs via Color Space Embeddings

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph's vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem.

cs.CG↗

arXiv2006

Guard Placement For Wireless Localization

Motivated by secure wireless networking, we consider the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by the interior of a polygon. Each localizer views an infinite wedge of the plane, and a device can prove membership in the secure region if it is inside the wedges for a set of localizers whose common intersection contains no points outside the polygon. This model leads to a broad class of new art gallery type problems, for which we provide upper and lower bounds.

cs.CG↗

arXiv2005

Delta-confluent Drawings

We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of Delta-confluent graphs are also given.

cs.CG↗

arXiv2005

The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries.

cs.CG↗

arXiv2005

Skip-Webs: Efficient Distributed Data Structures for Multi-Dimensional Data Sets

We present a framework for designing efficient distributed data structures for multi-dimensional data. Our structures, which we call skip-webs, extend and improve previous randomized distributed data structures, including skipnets and skip graphs. Our framework applies to a general class of data querying scenarios, which include linear (one-dimensional) data, such as sorted sets, as well as multi-dimensional data, such as d-dimensional octrees and digital tries of character strings defined over a fixed alphabet. We show how to perform a query over such a set of n items spread among n hosts using O(log n / log log n) messages for one-dimensional data, or O(log n) messages for fixed-dimensional data, while using only O(log n) space per host. We also show how to make such structures dynamic so as to allow for insertions and deletions in O(log n) messages for quadtrees, octrees, and digital tries, and O(log n / log log n) messages for one-dimensional data. Finally, we show how to apply a blocking strategy to skip-webs to further improve message complexity for one-dimensional data when hosts can store more data.

cs.DC↗

arXiv2005

Confluent Layered Drawings

We combine the idea of confluent drawings with Sugiyama style drawings, in order to reduce the edge crossings in the resultant drawings. Furthermore, it is easier to understand the structures of graphs from the mixed style drawings. The basic idea is to cover a layered graph by complete bipartite subgraphs (bicliques), then replace bicliques with tree-like structures. The biclique cover problem is reduced to a special edge coloring problem and solved by heuristic coloring algorithms. Our method can be extended to obtain multi-depth confluent layered drawings.

cs.CG↗

arXiv2005

Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.

cs.DS↗

arXiv2003

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.

cs.CG↗

arXiv2002

Confluent Drawings: Visualizing Non-planar Diagrams in a Planar Way

In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This approach allows us to draw, in a crossing-free manner, graphs--such as software interaction diagrams--that would normally have many crossings. The main idea of this approach is quite simple: we allow groups of edges to be merged together and drawn as "tracks" (similar to train tracks). Producing such confluent diagrams automatically from a graph with many crossings is quite challenging, however, so we offer two heuristic algorithms to test if a non-planar graph can be drawn efficiently in a confluent way. In addition, we identify several large classes of graphs that can be completely categorized as being either confluently drawable or confluently non-drawable.

cs.CG↗