2254306
An efficient direct approach for computing shortest rectilinear paths among obstacles in a two-layer interconnection model
In this paper, we present a direct approach for routing a shortest rectilinear path between two points among a set of rectilinear obstacles in a two-layer interconnection model that is used for VLSI routing applications. The previously best known direct approach for this problem takes O(nlog^2n) time and O(nlogn) space, where n is the total number of obstacle edges. By using integer data structures and an implicit graph representation scheme (i.e., a generalization of the distance table method), we improve the time bound to O(nlog^3^/^2n) while still maintaining the O(nlogn) space bound. Comparing with the indirect approach for this problem, our algorithm is simpler to implement and is probably faster for a quite large range of input sizes.
14297439
Geometric permutations of high dimensional spheres
We prove the maximum number of geometric permutations, induced by line transversals to a set of <i>n</i> pairwise disjoint congruent spheres in <i>R<sup>d</sup></i> with <i>d</i> ⪈ 3, is no more than 4 when <i>n</i> is sufficiently large, achieving the best known upper bound for this problem. We also prove the maximum number of geometric permutations of a set of <i>n</i> noncongruent spheres of bounded radius ratio in R<sup>d</sup>, <i>d</i> ⪈ 3, is at most 2<sup>[√2<i>M</i>]+1</sup>, where <i>M</i> is the ratio or the largest radius and the smallest radius. Our result settles a conjecture in combinatorial geometry.
29728094
Graph Bandwidth of Weighted Caterpillars
Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars and general graphs. More specifically, we show that the GBM problem on caterpillars with hair-length at most 2 and the GBM problem on star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log(nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum wedge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm and some experimental results. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of c log(n) of the lower bound for a small number c, which is consistent with the inapproximability results of this problem (i.e., no constant approximation for the GBM problem unless P = NP). © 2006 Published by Elsevier B.V.
28240465
Motion Tracking and Intensity Surface Recovery in Microscopic Nuclear Images
Current techniques for microscopic imaging do not provide necessary spatial and temporal resolutions for real time visualization of the nucleus. Images can only be acquired in time lapse mode, leading to significant loss of information between image frames. Such data, if available, can be extremely helpful in the study of nuclear organization and function. In this paper, we present a gamut of geometric-technique-based approaches for solving the problem. Our techniques, working together, can effectively recover complicated motion and deformation as well as the change of intensity surfaces from pairs of images in a microscopic image sequence, and has low time complexity, particularly desirable by many biological applications where large amount of DNA need to be processed. These techniques are also readily applicable to other types of images for reconstructing motion and intensity surfaces of deformable objects.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
21098955
Topological Peeling and Implementation
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walkb y 10 - 15% in execution time.
10511708
Automatic diagnosis and response to memory corruption vulnerabilities
Cyber attacks against networked computers have become relentless in recent years. The most common attack method is to exploit memory corruption vulnerabilities such as buffer overflow and format string bugs. This paper presents a technique to automatically identify both known and unknown memory corruption vulnerabilities. Based on the observation that a randomized program usually crashes upon a memory corruption attack, this technique uses the crash as a trigger to initiate an automatic diagnosis algorithm. The output of the diagnosis includes the instruction that is tricked to corrupt data, the call stack at the time of corruption, and the propagation history of corrupted data. These results provide useful information in fixing the vulnerabilities. Moreover, the diagnosis process also generates a signature of the attack using data/address values embedded in the malicious input message, and is used to block future attacks. Such a signature is further associated with the program execution state to reduce false positives without decreasing the detection rate. The proposed techniques enable the development of a decentralized self-diagnosing and self-protecting defense mechanism for networked computers. We report the implementation experience and experimental evaluation of a prototype system on Linux.
8865153
Validating UML models against architectural profiles
The Unified Modeling Language (UML) has become a widely adopted standard in the software industry. While UML has established itself in detailed software design, its usage as an architecture description language is still taking its shape. In particular, there is a growing need for techniques to define domain specific architectural constraints and conventions in UML. We address this issue by adopting the concept of UML profiles for architectural design. Architectural profiles are specialized for describing and constraining software architecture descriptions for a given domain. We argue that these profiles represent an appropriate abstraction level to elaborate architectural constraints and conventions. We present a general schema for arranging architectural profiles and a set of conformance rules that define how these profiles are interpreted, constituting a profile definition language for validating architectural design. We introduce a tool for performing architectural validation and discuss the results of our initial case studies.
8575653
Using Shortest Path Algorithms to Identify Criminal Associations
Frequently in criminal investigations, law enforcement agencies face the problem of identifying associations between a group of entities such as individuals and organizations. In this paper we present a link analysis technique to solve such a problem. This approach uses shortest path algorithms to find the strongest associations between two or more given entities. The experimental results have demonstrated that our approach is potentially useful in terms of quality and efficiency. Specifically, we found that the two-tree Priority-First Search algorithm in most cases was the fastest algorithm to find shortest paths and the paths found consisted of meaningful criminal associations around 80 percent of the time.
11532584
Sequentially t-Diagnosable Systems: A Characterization and Its Applications
In the system level fault diagnosis area, the fundamental problem of characterizing sequentially t-diagnosable systems in the PMC model has remained open for more than two decades. We resolve this problem by providing a complete characterization of such systems. Our solution to the characterization problem leads to the correct identification of optimal sequentially t-diagnosable D/sub /spl delta/,k/ systems. Given a set of n units where n=2t+1, an optimal D/sub /spl delta/,k/ system can be constructed with just n([(t+2)/3]) tests, rather than n([t/2]+1) tests-a previously misjudged bound. An efficient algorithm for identifying the set of faulty units in a sequentially t-diagnosable D/sub /spl delta/,k/ system is given along the line of the proposed characterization, which is linear with respect to the number of tests in the system. >
43179863
Analyzing Terrorist Networks: A Case Study of the Global Salafi Jihad Network
It is very important for us to understand the functions and structures of terrorist networks to win the battle against terror. However, previous studies of terrorist network structure have generated little actionable results. This is mainly due to the difficulty in collecting and accessing reliable data and the lack of advanced network analysis methodologies in the field. To address these problems, we employed several advance network analysis techniques ranging from social network analysis to Web structural mining on a Global Salafi Jihad network dataset collected through a large scale empirical study. Our study demonstrated the effectiveness and usefulness of advanced network techniques in terrorist network analysis domain. We also introduced the Web structural mining technique into the terrorist network analysis field which, to the best our knowledge, has never been used in this domain. More importantly, the results from our analysis provide not only insights for terrorism research community but also empirical implications that may help law-reinforcement, intelligence, and security communities to make our nation safer.