37965905
Rectilinear Paths among Rectilinear Obstacles
Given a set of obstacles and two distinguished points in the plane the problem of finding a collision-free path subject to a certain optimization function is a fundamental problem that arises in many fields, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinear domain in which the goal path to be computed and the underlying obstacles are all rectilinearly oriented, i.e., the segments are either horizontal or vertical. We consider different routing environments, and various optimization criteria pertaining to VLSI design, and provide a survey of results that have been developed in the past, present current results and give open problems for future research.
15124242
Solving the all-pair shortest path query problem on interval and circular-arc graphs
In this paper, we study the following all-pair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed eeciently (both sequentially and in parallel). We show that, after sorting the input intervals by their endpoints, a data structure can be constructed sequentially in O(n) time and O(n) space; using this data structure, each query on the length of the shortest path between any two intervals can be answered in O(1) time, and each query on the actual shortest path can be answered in O(k) time, where k is the number of intervals on that path. Furthermore, this data structure can be constructed optimally in parallel, in O(log n) time using O(n= log n) CREW PRAM processors; each query on the actual shortest path can be answered in O(1) time using k processors. Our techniques can be extended to solving the all-pair shortest path query problem on circular-arc graphs, both sequentially and in parallel, in the same complexity bounds. As an immediate consequence of our results, we improve by a factor of n the space complexity of the previously best known sequential all-pair shortest path algorithm for unweighted interval graphs.
10484740
Labeling Points on a Single Line
In this paper, we consider a map labeling problem where the points to be labeled are restricted on a line. It is known that the 1d-4P and the 1d-4S unit-square label placement problem and the Slope-4P unit-square label placement problem can both be solved in linear time and the Slope-4S unit-square label placement problem can be solved in quadratic time in Ref. [8]. We extend the result to the following label placement problem: Slope-4P fixed-height (width) label or elastic label placement problem and present a linear time algorithm for it provided that the input points are given sorted. We further show that if the points are not sorted, the label placement problems have a lower bound of Ω(n log n), where n is the input size, under the algebraic computation tree model. Optimization versions of these point labeling problems are also considered.
9367228
Verifying Web applications using bounded model checking
The authors describe the use of bounded model checking (BMC) for verifying Web application code. Vulnerable sections of code are patched automatically with runtime guards, allowing both verification and assurance to occur without user intervention. Model checking techniques are relatively complex compared to the typestate-based polynomial-time algorithm (TS) we adopted in an earlier paper, but they offer three benefits - they provide counterexamples, more precise models, and sound and complete verification. Compared to conventional model checking techniques, BMC offers a more practical approach to verifying programs containing large numbers of variables, but requires fixed program diameters to be complete. Formalizing Web application vulnerabilities as a secure information flow problem with fixed diameter allows for BMC application without drawback. Using BMC-produced counterexamples, errors that result from propagations of the same initial error can be reported as a single group rather than individually. This offers two distinct benefits. First, together with the counterexamples themselves, they allow for more descriptive and precise error reports. Second, it allows for automated patching at locations where errors are initially introduced rather than at locations where the propagated errors cause problems. Results from a TS-BMC comparison test using 230 open-source Web applications showed a 41.0% decrease in runtime instrumentations when BMC was used. In the 38 vulnerable projects identified by TS, BMC classified the TS-reported 980 individual errors into 578 groups, with each group requiring a minimal set of patches for repair.
14910989
Geosheet: A Distributed Visualization Tool for Geometric Algorithms
GeoSheet (version 1.0) is an interactive visualization tool for visualizing geometric algorithms in distributed environments. It provides features such as interactive visualization of program states for debugging, high-level graphical input/output manipulation facilities for geometric objects, reuse of existing data structures and algorithms implementation, and more importantly distributed executions on heterogeneous machines at different sites. To minimize development effort of the tool we make use of existing software packages available in public domain. Specifically we extend Xfig with a message-driven interface and a socket-based interprocess communication (IPC) mechanism. This extended-Xfig is the backbone of this version of the tool. Object-oriented programming methodology is used to construct the visualization interface. By deriving from traditional data type and algorithm libraries, our abstract GeoObject representation super-classes are easy to use, easy to construct, and highly portable. Although GeoSheet is not restricted to a particular application domain or any programming language, this release only contains geometric algorithm implementations in C++ and LEDA. We hope that the geometric algorithm designers will find it useful when they develop their algorithms.
6056146
Critical area computation via Voronoi diagrams
In this paper, we present a new approach for computing the critical area for shorts in a circuit layout. The critical area calculation is the main computational problem in very large scale integration yield prediction. The method is based on the concept of Voronoi diagrams and computes the critical area for shorts (for all possible defect radii, assuming square defects) accurately in O(n log n) time, where n is the size of the input. The method is presented for rectilinear layouts and layouts containing edges of slope /spl plusmn/1. As a byproduct, we briefly sketch how to speed up the grid method of Wagner and Koren [1995].
12896882
Faster Gaussian Summation: Theory and Experiment
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).
19220261
Path protection and blocking probability minimization in optical networks
We study the problem of shared path protection in optical networks from the viewpoint of blocking probability minimization. Unlike the worst-case approach common in other studies, which typically deals with one failure at a time and requires recomputation of the protection paths after every failure, our framework assumes a fixed path protection strategy for every connection that does not change in response to failures in other connections, which is more realistic for networks with high failure rates. We study backup-path strategy configurations that minimize the blocking probability and derive various properties. We show that configurations which do not have partial overlaps among connections backup paths are optimal in a rather general sense. We discuss the minmax optimal configuration properties and present an efficient algorithm for finding it in a case of special interest, while showing it to be NP-hard in general. In addition, we discuss the properties of the game resulting if each connection chooses its backup path selfishly; we show it to belong to the class of potential games, well-studied in the game theory literature, and derive several further properties resulting from its specific structure.
45853491
Testing Finite-State Machines: State Identification and Verification
We study the complexity of two fundamental problems in the testing of finite-state machines. 1) Distinguishing sequences (state identification). We show that it is PSPACE-complete to determine whether a finite-state machine has a preset distinguishing sequence. There are machines that have distinguishing sequences, but only of exponential length. We give a polynomial time algorithm that determines whether a finite-state machine has an adaptive distinguishing sequence. (The previous classical algorithms take exponential time.) Furthermore, if there is an adaptive distinguishing sequence, then we give an efficient algorithm that constructs such a sequence of length at most n(n/spl minus/1)/2 (which is the best possible), where n is the number of states. 2) Unique input output sequences (state verification). It is PSPACE-complete to determine whether a state of a machine has a unique input output sequence. There are machines whose states have unique input output sequences but only of exponential length. >
6967475
Protocol System Integration, Interface and Interoperability
Heterogeneous network protocol systems are integrated together to fulfill complex tasks and their interoperability is a major hurdle for the network reliability and quality of services. We identify a new equivalence relation of states that preserves the integrated system interface behaviors. Based on this state equivalence we study the minimization of the system components with respect to their interfaces and design an efficient polynomial time minimization algorithm. We apply our technique to GMPLS protocols and obtain a significant state space reduction. We discuss integrated protocol system verification and interoperability testing with the minimized state system without resorting to the global state space information.
27807377
Protocol Feature Interactions
Feature interaction is one of the most intriguing problems in research and development of telecommunications systems. Features may interact and result in undesirable system behavior. Today the analysis of interactions is conducted in an ad hoc manner by subject matter experts. This leads to time-consuming feature design and testing without any interaction-free guarantee.