Efficient Testing Algorithm Research Articles

A Two-Dimensional Ellipse–Rectangle Intersection Test

We present an efficient algorithm for testing whether or not a filled rectangle and a filled ellipse intersect. The algorithm requires at most two evaluations of the quadratic polynomial that defines the ellipse and the execution of a few simple arithmetic expressions. The convexity and monotonicity properties of this polynomial are the main tools for the design of the algorithm.

Efficient march test for 3-coupling faults in random access memories

A new efficient march test algorithm for detecting the 3-coupling faults in Random Access Memories (RAM) is given in this paper. To reduce the length of the test algorithm only the 3-coupling faults between physically adjacent memory cells have been considered. The proposed test algorithm needs 38N operations. We have proved, using an Eulerian graph model, that the algorithm detects all non-interacting coupling faults. This paper also comprises a study about the ability of the algorithm to cover the interacting coupling faults. Simulation results with regard to the coupling fault coverage of the march tests, obtained based on a fault injection mechanism, are also presented in this paper.

Plant Template Generation for Time-Delay Systems in Quantitative Feedback Control Theory

In this paper we present a necessary and sufficient condition for the zero inclusion of the value set f(T,Q) = f(τ,q) : τϵT:=τ−,τ+, q ϵ Q:=∏k=0m−1qk−, qk+, where f(τ, q) = g(q) + h(q)e-jτw with g(q) and h(q) being both complex-valued affine functions of the m-dimensional real vector q and ω a fixed frequency. Based on this condition we develop an efficient zero inclusion test algorithm for the value set f(T, Q). This zero inclusion test algorithm is applied along with a pivoting procedure to generate plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. To illustrate the efficiency of the algorithm, an example is provided.

Graph Isomorphism and Identification Matrices: Sequential Algorithms

A number of properties on identification matrices are presented here. For example, we prove that adjacency matrices are identification matrices for all bipartite graphs. We also study the application of the theory of identification matrices to solving the graph isomorphism problem, a famous open problem. We show that, given two graphs represented by two identification matrices with respect to a certain relation, isomorphism can be decided efficiently if at least one matrix satisfies the consecutive 1's property or a relaxed property thereof. Graphs which have identification matrices satisfying the consecutive 1's property include, among others, proper interval graphs and doubly convex bipartite graphs. This work leads to the first efficient isomorphism testing algorithms for certain classes of graphs and more efficient algorithms for some other classes of graphs. The algorithms for some classes of graphs including convex bipartite graphs run in linear time and are optimal.

Computing frequency responses of uncertain systems

A numerical approach is proposed for computing the frequency-response templates of a class of rational transfer functions whose coefficients are affine functions of some interval parameters. This approach is based on characterizing the template as the set of points in the complex plane that make the value set of a certain polytope of polynomials to include the origin. With this characterization, the proposed approach traces out the boundary of the frequency-response template corresponding to a single frequency by using a simple pivoting procedure along with an efficient zero-inclusion test algorithm.

Optimal Upward Planarity Testing of Single-Source Digraphs

A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of single-source digraphs; we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a single-source digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with $n \log \log n/\log n$ processors, using O(n,) space. The algorithm also constructs an upward planar drawing if the test is successful. The previously known best result is an O(n2)-time algorithm by Hutton and Lubiw [Proc. 2nd ACM--SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1991, pp. 203--211]. No efficient parallel algorithms for upward planarity testing were previously known.

Graph isomorphism and identification matrices: parallel algorithms

In this paper, we explore some properties of identification matrices and exhibit some uses of identification matrices in studying the graph isomorphism problem, a famous open problem. We show that, given two graphs in the form of a certain identification matrix, isomorphism can be tested efficiently in parallel if at least one matrix satisfies the circular 1s property, and more efficiently in parallel if at least one matrix satisfies the consecutive 1s property. Graphs which have identification matrices satisfying the consecutive 1s property include, among others, proper interval graphs and doubly convex bipartite graphs. The result presented here substantially broadens the class of graphs for which there are known efficient parallel isomorphism testing algorithms.

The Emerging Genetic Diversity of HIV

The discovery of highly divergent strains of human immunodeficiency virus (HIV) not reliably detected by a number of commonly used diagnostic tests has underscored the need for effective surveillance to track HIV variants and to direct research and prevention activities. Pathogens such as HIV that mutate extensively present significant challenges to effective monitoring of pathogens and to disease control. To date, relatively few systematic large-scale attempts have been made to characterize and sequence HIV isolates. For most of the world, including the United States, information on the distribution of HIV strains among different population groups is limited. We describe herein the implications resulting from the rapid evolution of HIV and the need for systematic surveillance integrated with laboratory science and applied research. General surveillance guidelines are provided to assist in identifying population groups for screening, in applying descriptive epidemiology and systematic sampling, and in developing and evaluating efficient laboratory testing algorithms. Timely reporting and dissemination of data is also an important element of surveillance efforts. Ultimately, the success of global surveillance network depends on collaboration and on coordination of clinical, laboratory, and epidemiologic efforts.

Testing orthogonal shapes

A testing algorithm takes a model and produces a set of points that can be used to test whether or not an unknown object is sufficiently similar to the model. A testing algorithm performs a complementary task to that performed by a learning algorithm, which takes a set of examples and builds a model that succinctly describes them. Testing can also be viewed as a type of geometric probing that uses point probes (i.e. test points) to verify that an unknown geometric object is similar to a given model. In this paper we examine the problem of verifying orthogonal shapes using test points. In particular, we give testing algorithms for sets of disjoint rectangles in two and higher dimensions and for general orthogonal shapes in 2-D and 3-D. This work is a first step towards developing efficient testing algorithms for objects with more general shapes, including those with non-orthogonal and curved surfaces.

Steiner Distance-Hereditary Graphs

Let G be a connected graph and $S \subseteq V( G )$. Then the Steiner distance of S in G, denoted by $d_G ( S )$, is the smallest number of edges in a connected subgraph of G that contains S. A connected graph G is k-Steiner distance-hereditary, $k \geq 2$, if, for every $S \subseteq V( G )$ such that $|S| = k$ and every connected induced subgraph H of G containing $S,d_H ( S ) = d_G ( S )$. It is shown that if G is 2-Steiner distance-hereditary, then G is k-Steiner distance-hereditary for all $k \geq 2$. Furthermore, it is shown that if G is k-Steiner distance-hereditary $( k \geq 3 )$, then G need not be $( k - 1 )$-Steiner distance-hereditary. An efficient algorithm for determining the Steiner distance of a set of k vertices in a k-Steiner distance-hereditary graph is discussed, and a characterization of 2-Steiner distance-hereditary graphs that leads to an efficient algorithm for testing whether a graph is 2-Steiner distance-hereditary is given.

Efficient Detection and Protection of Information in Cross Tabulated Tables I: Linear Invariant Test

To protect sensitive information in a cross tabulated table, it is a common practice to suppress some of the cells in the table. A linear combination of suppressed cells is called a linear invariant if the combination has a unique feasible value. Intuitively, the information contained in an invariant is not protected even though the values of the suppressed cells are not disclosed. This paper gives a surprisingly efficient algorithm for testing whether a linear combination of suppressed cells is an invariant. In sequential computation, the algorithm runs in optimal linear time. In parallel computation, the algorithm runs in polylogarithmic time using a polynomial number of processors on a parallel random access machine. The algorithm exploits a linear algebraic structure of directed and undirected cycles in a mixed graph induced by a given table. This new structure also plays a crucial role in subsequent papers on other aspects of detecting and protecting sensitive information in a cross tabulated table.

Preservation of integrity constraints in definite DATALOG programs

Given a program P and two sets IC and IC′ of integrity constraints, IC uniformly implies IC′ in P if whenever an (input) database I defined on predicates of P satisfies IC then the (output) database computed by P from I satisfies IC′. P preserves IC if IC uniformly implies IC in P. We consider only definite DATALOG programs. We show that testing preservation of downward-closed integrity constraints can be simplified to the case of single-rule programs that are computed in a “nonrecursive manner”. Specially, we present an efficient test algorithm when constraints are equality-generating dependencies. We also show that the uniform implication problem can be similarly simplified if IC is preserved and all given constraints are downward-closed. Our results generalize dependency-preserving database schemes by considering mappings defined by arbitrary definite DATALOG programs and more general integrity constraints.

Autoepistemic logic

Autoepistemic logic is one of the principal modes of nonmonotonic reasoning. It unifies several other modes of nonmonotonic reasoning and has important application in logic programming. In the paper, a theory of autoepistemic logic is developed. This paper starts with a brief survey of some of the previously known results. Then, the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory. A notion similar to set-theoretic forcing is introduced. Expansions of autoepistemic theories are also investigated. Expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation. Theories that have expansions are characterized, and a normal form that allows the description of all expansions of a theory is introduced. Our results imply algorithms to determine whether a theory has a unique expansion. Sufficient conditions (stratification) that imply existence of a unique expansion are discussed. The definition of stratified theories is extended and (under some additional assumptions) efficient algorithms for testing whether a theory is stratified are proposed. The theorem characterizing expansions is applied to two classes of theories, K 1 -theories and ae-programs. In each case, simple hypergraph characterization of expansions of theories from each of these classes is given. Finally, connections with stable model semantics for logic programs with negation is discussed. In particular, it is proven that the problem of existence of stable models is NP-complete.— Authors' Abstract

Efficient Parallel Algorithms for Testingkand Finding Disjoints-tPaths in Graphs

An efficient parallel algorithm for testing whether a graph G is k-vertex connected is presented. The algorithm runs in $O(k^2 \log n)$ time and uses $(n + k^2 )kC(n,m)$ processors on a CROW PRAM, where n and m are the number of vertices and edges of G, and $C(n,m)$ is the number of processors required to compute the connected components of G in logarithmic time. For fixed k, the algorithm runs in logarithmic time and uses $nC(n,m)$ processors. To develop our algorithm, an efficient parallel algorithm is designed for the following disjoint s-t paths problem. Given a graph G, and two specified vertices s and t, find k vertex disjoint paths between s and t, if they exist. If no such paths exist, find a set of at most $k-1$ vertices whose removal disconnects s and t. The parallel algorithm for this problem runs in $O(k^2 \log n)$ time and uses $kC(n,m)$ processors. The way to modify the algorithm to find k-edge disjoint paths, if they exist, is shown. This yields an efficient parallel algorithm for testing w...

Testing of interconnection circuits in wafer-scale arrays

An efficient testing algorithm for interconnection circuits, including programmable switches and data links in wafer-scale reconfigurable arrays, is presented. Faulty programmable switches or data links are eliminated by finding fault-free paths in the switch grid obtained by isolating all computing units from the rest of a reconfigurable array. No internal test points are assumed. The algorithm is shown to achieve very high performance, even if cell yield is low.

Exploitation of parallelism in VLSI array testing

Testing of VLSI/WSI arrays using the spiral testing method is time-consuming due to its sequential nature. In this paper, we propose an efficient testing algorithm which reduces the testing time considerably and requires little hardware overhead. Fault-free data paths are identified first to obtain a high degree of parallelism in cell function unit testing. Cell functional units are then tested by using signature comparisons. Faulty cells determined to be fault-free due to fault masking are removed by subsequent comparisons of responses for every test input. A fairly general fault model is used to cover the faults in the switches and data links as well as the cell functional units.

Hierarchies and planarity theory

In diagrammatic representations of hierarchies the minimization of the number of crossings between edges is a well-known criterion for improving readability. An efficient algorithm for testing if a hierarchy is planar (i.e. if it can be drawn without edge crossings) is proposed. A complete combinatorial characterization of the class of planar hierarchies is also given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Evaluation and comparison of two efficient probabilistic primality testing algorithms

We analyse two recent probabilistic primality testing algorithms; the first one is derived from Miller [6] in a formulation given by Rabin [7], and the second one is from Solovay and Strassen [9]. Both decide whether or not an odd number n is prime in time O( m, log n M( n)) with an error probability less than α m , for some 0≤a< 1 2 . Our comparison shows that the first algorithm is always more efficient than the second, both in probabilistic and algorithmic terms.