Results 21  30
of
44
The Test Suite Generation Problem: Optimal Instances and Their Implications
"... In the test suite generation problem (TSG) for software systems, I is a set of n input parameters where each I ∈ I has κ(I) data values, and O is a collection of subsets of I where the interactions of the parameters in each O ∈ O are thought to affect the outcome of the system. A test case for (I, O ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In the test suite generation problem (TSG) for software systems, I is a set of n input parameters where each I ∈ I has κ(I) data values, and O is a collection of subsets of I where the interactions of the parameters in each O ∈ O are thought to affect the outcome of the system. A test case for (I, O, κ) is an ntuple (t1, t2,..., tn) that specifies the value of each input parameter in I. The goal is to generate a smallestsized test suite (i.e., a set of test cases) that covers all combinations of each O ∈ O. The decision version of TSG is known to be NPcomplete. In this paper, we present new families of (I, O, κ) for which optimal test suites can be constructed efficiently. They differ from the ones already known by the way we characterize (I, O) and κ. We then use these instances to generate test suites for arbitrary software systems. When each O ∈ O has O  = 2, the sizes of the test suite are guaranteed to be at most ⌈log 2 n ⌉ × OP T, matching the current best bound for this problem. Our constructions utilize the structure of (I, O) and κ; consequently, the less “complex ” (I, O) and κ are, the better are the bounds on the sizes of the test suites. 1
Bounded VCdimension implies a fractional Helly theorem
, 2002
"... We prove that every set system of bounded VCdimension has a fractional Helly property. More precisely, if the dual shatter function of a set system F is bounded by o(m ), then F has fractional Helly number k. This means that for every ff ? 0 there exists a fi ? 0 such that if F 1 ; F 2 ; : : ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We prove that every set system of bounded VCdimension has a fractional Helly property. More precisely, if the dual shatter function of a set system F is bounded by o(m ), then F has fractional Helly number k. This means that for every ff ? 0 there exists a fi ? 0 such that if F 1 ; F 2 ; : : : ; Fn 2 F are sets with i2I F i 6= ; for at least sets I ` f1; 2; : : : ; ng of size k, then there exists a point common to at least fin of the F i . This further implies a (p; k)theorem: for every F as above and every p k there exists T such that if G ` F is a finite subfamily where among every p sets, some k intersect, then G has a transversal of size T . The assumption about bounded dual shatter function applies, for example, to families of sets in R definable by a bounded number of polynomial inequalities of bounded degree; in this case, we obtain fractional Helly number d+1.
Discrepancy of Point Sequences on Fractal Sets
"... We consider asymptotic bounds for the discrepancy of point sets on a class of fractal sets. By a method of R. Alexander, we prove that for a wide class of fractals, the L 2 discrepancy (and consequently also the worstcase discrepancy) of an Npoint set with respect to halfspaces is at least of the ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We consider asymptotic bounds for the discrepancy of point sets on a class of fractal sets. By a method of R. Alexander, we prove that for a wide class of fractals, the L 2 discrepancy (and consequently also the worstcase discrepancy) of an Npoint set with respect to halfspaces is at least of the order N^(1/21/(2s)) , where s is the Hausdorff dimension of the fractal. We also show that for many fractals, this bound is tight for the L 2 discrepancy. Determining the correct order of magnitude of the worstcase discrepancy remains a challenging open problem.
Quantum Lower Bounds by Entropy Numbers
, 2006
"... We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the nth minimal error in the quantum setting of informationbased complexity. As an application, we improve some lower bounds on quantum approximation of embeddings between finite dimensional Lp ..."
Abstract
 Add to MetaCart
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the nth minimal error in the quantum setting of informationbased complexity. As an application, we improve some lower bounds on quantum approximation of embeddings between finite dimensional Lp spaces and of Sobolev embeddings. 1
Discrepancy after adding . . .
"... We show that the hereditary discrepancy of a hypergraph F on n pointsincreases by a factor of at most O(log n) when one adds a new edge to F. ..."
Abstract
 Add to MetaCart
We show that the hereditary discrepancy of a hypergraph F on n pointsincreases by a factor of at most O(log n) when one adds a new edge to F.
Mergeable Coresets
, 2011
"... We study the mergeability of data summaries. Informally speaking, mergeability requires that, given two summaries on two data sets, there is a way to merge the two summaries into a summary on the two data sets combined together, while preserving the error and size guarantees. This property means tha ..."
Abstract
 Add to MetaCart
We study the mergeability of data summaries. Informally speaking, mergeability requires that, given two summaries on two data sets, there is a way to merge the two summaries into a summary on the two data sets combined together, while preserving the error and size guarantees. This property means that the summary can be treated like other algebraic objects such as sum and max, which is especially useful for computing summaries on massive distributed data. Many data summaries are trivially mergeable by construction, most notably those based on linear transformations. But some other fundamental ones like those for heavy hitters and quantiles, are not (known to be) mergeable. In this paper, we demonstrate that these summaries are indeed mergeable or can be made mergeable after appropriate modifications. Specifically, we show that for εapproximate heavy hitters, there is a deterministic mergeable summary log(εn)) that has a restricted form of mergeability, and a randomized one of size O ( 1 ε ε) with full mergeability. We also extend our results to geometric summaries such as εapproximations and εkernels. of size O(1/ε); for εapproximate quantiles, there is a deterministic summary of size O ( 1 ε 1
Modelbased TestCase Generation for Testing Robustness of Vision Components of Robotic Systems Extended Abstract
, 2013
"... Abstract. This extended abstract outlines a modelbased approach for generating test data to assess the robustness of computer vision (CV) solutions with respect to a given task or application. The outlined approach enables the automatic generation of test data with a measurable coverage of optical ..."
Abstract
 Add to MetaCart
Abstract. This extended abstract outlines a modelbased approach for generating test data to assess the robustness of computer vision (CV) solutions with respect to a given task or application. The outlined approach enables the automatic generation of test data with a measurable coverage of optical situations both typical as well as critical for a given application. In addition, expected results are generated, all with almost no manual effort. 1
QUASIMONTE CARLO METHODS IN FINANCE
"... We review the basic principles of QuasiMonte Carlo (QMC) methods, the randomizations that turn them into variancereduction techniques, and the main classes of constructions underlying their implementations: lattice rules, digital nets, and permutations in different bases. QMC methods are designed t ..."
Abstract
 Add to MetaCart
We review the basic principles of QuasiMonte Carlo (QMC) methods, the randomizations that turn them into variancereduction techniques, and the main classes of constructions underlying their implementations: lattice rules, digital nets, and permutations in different bases. QMC methods are designed to estimate integrals over the sdimensional unit hypercube, for moderate or large (perhaps infinite) values of s. In principle, any stochastic simulation whose purpose is to estimate an integral fits this framework, but the methods work better for certain types of integrals than others (e.g., if the integrand can be well approximated by a sum of lowdimensional smooth functions). Such QMCfriendly integrals are encountered frequently in computational finance and risk analysis. We give examples and provide computational results that illustrate the efficiency improvement achieved. 1
Random numbers
"... have a peculiar power, even when they are only pseudoor quasirandom In the early 1990s Spassimir Paskov, then a graduate student at Columbia University, began analyzing an exotic financial instrument called a collateralized mortgage obligation, or CMO, issued by the investment bank Goldman Sachs. Th ..."
Abstract
 Add to MetaCart
have a peculiar power, even when they are only pseudoor quasirandom In the early 1990s Spassimir Paskov, then a graduate student at Columbia University, began analyzing an exotic financial instrument called a collateralized mortgage obligation, or CMO, issued by the investment bank Goldman Sachs. The aim was to estimate the current value of the CMO, based on the potential future cash flow from thousands of 30year mortgages. This task wasn’t just a matter of applying
Optimizationbased Design of PlantFriendly Input Signals for ModelonDemand Estimation and Model Predictive Control
"... Abstract — The design of constrained, “plantfriendly ” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for datacentric estimation and control methods, where uniform coverage of the output sta ..."
Abstract
 Add to MetaCart
Abstract — The design of constrained, “plantfriendly ” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for datacentric estimation and control methods, where uniform coverage of the output statespace contributes greatly to good performance. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal that achieves a desirable balance between high and low gain directions, an important consideration when identifying strongly interactive multivariable systems. The solution involves very little user intervention and has significant benefits compared to multisine signals that minimize crest factor. The usefulness of this problem formulation is shown by applying it to a case study involving composition control of a binary distillation column. I.