Showing papers by "Michael T. Goodrich published in 2002"

Efficient packet marking for large-scale IP traceback

Abstract: We present a new approach to IP traceback based on the probabilistic packet marking paradigm. Our approach, which we call randomize-and-link, uses large checksum cords to "link" message fragments in a way that is highly scalable, for the checksums serve both as associative addresses and data integrity verifiers. The main advantage of these checksum cords is that they spread the addresses of possible router messages across a spectrum that is too large for the attacker to easily create messages that collide with legitimate messages. Our methods therefore scale to attack trees containing hundreds of routers and do not require that a victim know the topology of the attack tree a priori. In addition, by utilizing authenticated dictionaries in a novel way, our methods do not require routers sign any setup messages individually.

An Efficient Dynamic and Distributed Cryptographic 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. 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.

Efficiently approximating polygonal paths in three and higher dimensions

Abstract: We present efficient algorithms for solving polygonal-path approximation problems in three and higher dimensions. Given an n -vertex polygonal curve P in \R d , d \geq 3 , we approximate P by another poly- gonal curve P' of m ≤ n vertices in \R d such that the vertex sequence of P' is an ordered subsequence of the vertices of P . The goal is either to minimize the size m of P' for a given error tolerance \eps (called the min-\# problem), or to minimize the deviation error \eps between P and P' for a given size m of P' (called the min- \eps problem). Our techniques enable us to develop efficient near-quadratic-time algorithms in three dimensions and subcubic-time algorithms in four dimensions for solving the min-\# and min-\eps problems. We discuss extensions of our solutions to d -dimensional space, where d > 4 , and for the L 1 and L ∈ fty metrics.

Optimizing area and aspect ratio in straight-line orthogonal tree drawings

Abstract: We investigate the problem of drawing an arbitrary n-node binary tree orthogonally and upwardly in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as a fixed constant or a parameter under the user's control. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call "subtree separation". Our drawings require O(n logn) area, which we show is optimal to within constant factors in the worst case (i.e. there are trees that need Ω(n logn) area for any upward orthogonal straight-line drawing with good aspect ratio). An improvement for non-upward drawings is briefly mentioned.

Three-Dimensional Layers of Maxima

Abstract: We present an O(n log n)-time algorithm to solve the three-dimensional layers-of-maxima problem, an improvement over the prior O(n log n log log n)-time solution. A previous claimed O(n log n)-time solution due to Atallah, Goodrich, and Ramaiyer [SCG'94] has technical flaws. Our algorithm is based on a common framework underlying previous work, but to implement it we devise a new data structure to solve a special case of dynamic planar point location in a staircase subdivision. Our data structure itself relies on a new extension to dynamic fractional cascading that allows vertices of high degree in the control graph.

Biased Skip Lists

Abstract: We design a variation of skip lists that performs well for generally biased access sequences. Given n items, each with a positive weight wi, 1 ? i ? n, the time to access item i is O(1 + log W/wi), where W = ?i = 1n wi; the data structure is dynamic. We present deterministic and randomized variations, which are nearly identical; the deterministic one simply ensures the balance condition that the randomized one achieves probabilistically. We use the same method to analyze both.

Graph drawing : 10th International Symposium, GD 2002, Irvine, CA, USA, August 26-28, 2002 : revised papers

Abstract: Papers.- Sketch-Driven Orthogonal Graph Drawing.- Maintaining the Mental Map for Circular Drawings.- Graphs, They Are Changing.- Drawing Graphs on Two and Three Lines.- Path-Width and Three-Dimensional Straight-Line Grid Drawings of Graphs.- Drawing Outer-Planar Graphs in O(n log n )Area.- Computing Labeled Orthogonal Drawings.- Computing and Drawing Isomorphic Subgraphs.- A Group-Theoretic Method for Drawing Graphs Symmetrically.- A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem.- Geometric Systems of Disjoint Representatives.- An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization.- Simple and Efficient Bilayer Cross Counting.- Orthogonal 3D Shapes of Theta Graphs.- Separating Thickness from Geometric Thickness.- Book Embeddings and Point-Set Embeddings of Series-Parallel Digraphs.- Compact Encodings of Planar Orthogonal Drawings.- Fractional Lengths and Crossing Numbers.- Drawing Directed Graphs Using One-Dimensional Optimization.- Graph Drawing by High-Dimensional Embedding.- Advances in C-Planarity Testing of Clustered Graphs.- HGV: A Library for Hierarchies, Graphs, and Views.- Rectangular Drawings of Planar Graphs.- Extended Rectangular Drawings of Plane Graphs with Designated Corners.- RINGS: A Technique for Visualizing Large Hierarchies.- Applying Crossing Reduction Strategies to Layered Compound Graphs.- Crossing Reduction by Windows Optimization.- Geometric Graphs with No Self-intersecting Path of Length Three.- Two New Heuristics for Two-Sided Bipartite Graph Drawing.- Straight-Line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio.- Some Applications of Orderly Spanning Trees in Graph Drawing.- Improving Walker's Algorithm to Run in Linear Time.- Semi-dynamic Orthogonal Drawings of Planar Graphs.- Software Demonstrations.- Graph Layout for Workflow Applications with ILOG JViews.- InterViewer: Dynamic Visualization of Protein-Protein Interactions.- Some Modifications of Sugiyama Approach.- A Framework for Complexity Management in Graph Visualization.- A Partitioned Approach to Protein Interaction Mapping.- Camera Position Reconstruction and Tight Direction Networks.- Demonstration of a Preprocessor for the Spring Embedder.- Graph Drawing Contest.- Graph-Drawing Contest Report.- Invited Talks.- Techniques for Interactive Graph Drawing.- Drawing Venn Diagrams.

Three-dimensional layers of maxima

Abstract: We present an O(n log n)-time algorithm to solve the three-dimensional layers-of-maxima problem, an improvement over the prior O(n log n log log n)-time solution. A previous claimed O(n log n)-time solution due to Atallah, Goodrich, and Ramaiyer [SCG'94] has technical flaws. Our algorithm is based on a common framework underlying previous work, but to implement it we devise a new data structure to solve a special case of dynamic planar point location in a staircase subdivision. Our data structure itself relies on a new extension to dynamic fractional cascading that allows vertices of high degree in the control graph.

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

Abstract: 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.