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201. Biased covering arrays for progressive ranking and composition of Web Services

Author

Bryce, Renee C., Chen, Yinong, and Colbourn, Charles J.

Subjects
Computers and office automation industries, Engineering and manufacturing industries
Abstract

Byline: Renee C. Bryce, Yinong Chen, Charles J. Colbourn Service-oriented computing is a new software development paradigm that allows application builders to choose from many available services. The challenges are to efficiently determine which services are the most appropriate to combine into an application based on concerns such as functionalities, licensing costs, and known reliability. Group testing has addressed some issues on how to select a small subset of candidate services. We expand upon the group testing methodology with a greedy algorithm that generates biased covering arrays for interactive testing of the services selected by group testing.

Published
2007

220. Group divisible covering designs with block size four.

Author

Wei, Hengjia, Ge, Gennian, and Colbourn, Charles J.

Subjects
DIVISIBILITY groups, GENERALIZATION, DATA compression, EXISTENCE theorems, NUMBER theory
Abstract

Abstract: Group divisible covering designs (GDCDs) were introduced by Heinrich and Yin as a natural generalization of both covering designs and group divisible designs. They have applications in software testing and universal data compression. The minimum number of blocks in a k‐GDCD of type g u is a covering number denoted by C ( k , g u ). When k = 3, the values of C ( 3 , g u ) have been determined completely for all possible pairs ( g , u ). When k = 4, Francetić et al. constructed many families of optimal GDCDs, but the determination remained far from complete. In this paper, two specific 4‐IGDDs are constructed, thereby completing the existence problem for 4‐IGDDs of type ( g , h ) u. Then, additional families of optimal 4‐GDCDs are constructed. Consequently the cases for ( g , u ) whose status remains undetermined arise when g ≡ 7 mod 12 and u ≡ 3 mod 6, when g ≡ 11 , 14 , 17 , 23 mod 24 and u ≡ 5 mod 6, and in several small families for which one of g and u is fixed. [ABSTRACT FROM AUTHOR]

Published
2018
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221. Improved Strength Four Covering Arrays with Three Symbols.

Author

Maity, Soumen, Akhtar, Yasmeen, Chandrasekharan, Reshma C., and Colbourn, Charles J.

Subjects
MATHEMATICAL notation, DRUG use testing, COMPUTER software testing, MATHEMATICAL bounds, NUMBER theory
Abstract

A covering array t-CA(n, k, g), of size n, strength t, degree k, and order g, is a k×n array on g symbols such that every t×n sub-array contains every t×1 column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we present an algebraic construction that improves many of the best known upper bounds on n for covering arrays 4-CA(n, k, 3). The t-coverage of a testing array A is the number of distinct t-tuples contained in the column vectors of A divided by the total number of t-tuples. If the testing array is a covering array of strength t, its t-coverage is 100%. The covering arrays with budget constraints problem is the problem of constructing a testing array of size at most n having largest possible coverage, given values of t, k, g and n. This paper also presents several testing arrays with high 4-coverage. [ABSTRACT FROM AUTHOR]

Published
2018
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222. Locating one pairwise interaction: Three recursive constructions.

Author

Colbourn, Charles J. and Bingli Fan

Subjects
RECURSIVE functions, PAIRED comparisons (Mathematics), MATHEMATICAL complex analysis, HEURISTIC, MATHEMATICAL analysis
Abstract

In a complex component-based system, choices (levels) for components (factors) may interact to cause faults in the system behaviour. When faults may be caused by interactions among few factors at specific levels, covering arrays provide a combinatorial test suite for discovering the presence of faults. While well studied, covering arrays do not enable one to determine the specific levels of factors causing the faults; locating arrays ensure that the results from test suite execution suffice to determine the precise levels and factors causing faults, when the number of such causes is small. Constructions for locating arrays are at present limited to heuristic computational methods and quite specific direct constructions. In this paper three recursive constructions are developed for locating arrays to locate one pairwise interaction causing a fault. [ABSTRACT FROM AUTHOR]

Published
2017
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223. The 3-GDDs of type g³u².

Author

Colbourn, Charles J., Keranen, Melissa S., and Kreher, Donald L.

Subjects
DIGITAL divide, MATHEMATICAL decomposition, TRIANGLES, GRAPH theory, MATHEMATICAL analysis
Abstract

A 3-gdd of type g³u² exists if and only if g and u have the same parity, 3 divides u and u ≤ 3g. Such a 3-gdd of type g³u² is equivalent to an edge decomposition of Kg;g;g;u;u into triangles. [ABSTRACT FROM AUTHOR]

Published
2017
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225. Locating Arrays

Author

Aldaco, Abraham N., primary, Colbourn, Charles J., additional, and Syrotiuk, Violet R., additional

Published
2015
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226. DROP COST AND WAVELENGTH OPTIMAL TWO-PERIOD GROOMING WITH RATIO 4∗

Author

Jean-Claude Bermond, Colbourn, Charles J., Lucia Gionfriddo, Gaetano Quattrocchi, Ignasi Sau, Algorithms, simulation, combinatorics and optimization for telecommunications (MASCOTTE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Computer Science and Engineering [Tempe] (CIDSE), Arizona State University [Tempe] (ASU), Dipartimento di Matematica e Informatica (DMI), Università degli studi di Catania = University of Catania (Unict), Research Group on Graph Theory and Combinatorics [Barcelona], Universitat Politècnica de Catalunya [Barcelona] (UPC), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Università degli studi di Catania [Catania]

Subjects
[INFO.INFO-IU]Computer Science [cs]/Ubiquitous Computing, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Abstract

International audience; We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and $C=4$ and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.

Published
2010

229. Drop cost and wavelength optimal two-period grooming with ratio 4

Author

Jean-Claude Bermond, Colbourn, Charles J., Lucia Gionfriddo, Gaetano Quattrocchi, Ignasi Sau, Algorithms, simulation, combinatorics and optimization for telecommunications (MASCOTTE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Computer Science and Engineering [Tempe] (CIDSE), Arizona State University [Tempe] (ASU), Dipartimento di Matematica e Informatica (DMI), Università degli studi di Catania = University of Catania (Unict), Algorithmes, Graphes et Combinatoire (ALGCO), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Universidade Federal do Ceará = Federal University of Ceará (UFC), INRIA, Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Università degli studi di Catania [Catania], and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)

Subjects
SONET ADM, design theory, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], traffic grooming, optical networks, graph decomposition
Abstract

We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and $C=4$ and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.

Published
2009

240. Preface

Author

Colbourn, Charles J., primary and Mathon, Rudolf A., additional

Published
1987
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247. Routing in mobile aerial networks

Author

Syrotiuk, Violet R., Colbourn, Charles J., and Inria Sophia Antipolis-Méditerranée / I3s, Service Ist

Subjects
[INFO.INFO-MC] Computer Science [cs]/Mobile Computing, [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-PF] Computer Science [cs]/Performance [cs.PF]
Abstract

The problem of routing is unmanned aerial vehicles (UAVs) flying circular flight patterns equipped with directional antennas is considered. The active communication links are modelled as trigonometric functions of time.

Published
2003

248. Applications of combinatorial designs in computer science

Author

Colbourn, Charles J. and van Oorschot, Paul C.

Subjects
Combinatorics, Mathematical Models, Scientific Research, Nonnumerical Algorithms, Algorithm Analysis, Computer Science, Combinatorial number theory -- Models, Computer science -- Research
Published
1989

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