Charles J. Colbourn
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View article: Sets of mutually orthogoval projective and affine planes
Sets of mutually orthogoval projective and affine planes Open
A pair of planes, both projective or both affine, of the same order and on the same point set are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions …
View article: Bussey systems and Steiner's tactical problem
Bussey systems and Steiner's tactical problem Open
In 1853, Steiner posed a number of combinatorial (tactical) problems, which eventually led to a large body of research on Steiner systems. However, solutions to Steiner's questions coincide with Steiner systems only for strengths two and t…
View article: Guaranteeing Anonymity in Attribute-Based Authorization
Guaranteeing Anonymity in Attribute-Based Authorization Open
Attribute-based methods, such as attribute-based access control and attribute-based encryption, make decisions based on attributes possessed by a subject rather than the subject's identity. While this allows for anonymous authorization -- …
View article: Detecting arrays for effects of single factors
Detecting arrays for effects of single factors Open
Determining correctness and performance for complex engineered systems necessitates testing the system to determine how its behavior is impacted by factors and interactions among them. Of particular concern is to determine which settings o…
View article: Scalable level-wise screening experiments using locating arrays
Scalable level-wise screening experiments using locating arrays Open
Alternative design and analysis methods for screening experiments based on locating arrays are presented. The number of runs in a locating array grows logarithmically based on the number of factors, providing efficient methods for screenin…
View article: Sets of mutually orthogoval projective and affine planes
Sets of mutually orthogoval projective and affine planes Open
A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions f…
View article: Balanced and Swap-Robust Trades for Dynamical Distributed Storage
Balanced and Swap-Robust Trades for Dynamical Distributed Storage Open
Trades, introduced by Hedayat, are two sets of blocks of elements which may be exchanged (traded) without altering the counts of certain subcollections of elements within their constituent blocks. They are of importance in applications whe…
View article: Issue Information
Issue Information Open
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View article: A new approach to solving three combinatorial enumeration problems on planar graphs
A new approach to solving three combinatorial enumeration problems on planar graphs Open
The purpose of this paper is to show how the technique of delta-wye graph reduction provides an alternative method for solving three enumerative function evaluation problems on planar graphs. In particular, it is shown how to compute the n…
View article: Access Balancing in Storage Systems by Labeling Partial Steiner Systems
Access Balancing in Storage Systems by Labeling Partial Steiner Systems Open
Storage architectures ranging from minimum bandwidth regenerating encoded distributed storage systems to declustered-parity RAIDs can be designed using dense partial Steiner systems in order to support fast reads, writes, and recovery of f…
View article: Two‐stage algorithms for covering array construction
Two‐stage algorithms for covering array construction Open
Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to …
View article: Set-Codes with Small Intersections and Small Discrepancies
Set-Codes with Small Intersections and Small Discrepancies Open
We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is l…
View article: Robustness of Recovery in Locating Array-Based Screening Experiments
Robustness of Recovery in Locating Array-Based Screening Experiments Open
Locating arrays (LAs) are experimental designs for screening interactions in engineered systems. LAs are often highly unbalanced, requiring advanced techniques to recover the terms that significantly influence system performance. While per…
View article: Constructions of optimal orthogonal arrays with repeated rows
Constructions of optimal orthogonal arrays with repeated rows Open
We construct orthogonal arrays OA$_λ (k,n)$ (of strength two) having a row that is repeated $m$ times, where $m$ is as large as possible. In particular, we consider OAs where the ratio $m / λ$ is as large as possible; these OAs are termed …
View article: Subspace restrictions and affine composition for covering perfect hash families
Subspace restrictions and affine composition for covering perfect hash families Open
Covering perfect hash families provide a very compact representation of a useful family of covering arrays, leading to the best asymptotic upper bounds and fast, effective algorithms. Their compactness implies that an additional row in the…
View article: Issue Information
Issue Information Open
of Combinatorial Designs; 24 issues total, 2018): Institutional subscription prices for 2018 are: Print & Online: US$5763 (US), US$6322 (Rest of World), €4080 (Europe), £3229 (UK).Prices are exclusive of tax.Asia-Pacific GST, Canadian GST …
View article: Counting Subwords and Regular Languages
Counting Subwords and Regular Languages Open
Let $x$ and $y$ be words. We consider the languages whose words $z$ are those for which the numbers of occurrences of $x$ and $y$, as subwords of $z$, are the same (resp., the number of $x$'s is less than the number of $y$'s, resp., is les…
View article: Compressed Sensing With Combinatorial Designs: Theory and Simulations
Compressed Sensing With Combinatorial Designs: Theory and Simulations Open
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the per…
View article: Upper Bounds on the Size of Covering Arrays
Upper Bounds on the Size of Covering Arrays Open
Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN$(t,k,v)$, in a covering array for given values of the pa…
View article: Locating one pairwise interaction: Three recursive constructions
Locating one pairwise interaction: Three recursive constructions Open
In a complex component-based system, choices (levels) for components (factors) may interact tocause faults in the system behaviour. When faults may be caused by interactions among few factorsat specific levels, covering arrays provide a co…
View article: The 3-GDDs of type $g^3u^2$
The 3-GDDs of type $g^3u^2$ Open
A 3-GDD of type ${g^3u^2}$ exists if and only if $g$ and $u$ have the same parity, $3$ divides $u$ and $u\\leq 3g$.Such a 3-GDD of type ${g^3u^2}$ is equivalent to an edge decomposition of $K_{g,g,g,u,u}$ into triangles.