Efficient Greedy Algorithms with Accuracy Guarantees for Combinatorial Restrictions

The effective construction of covering arrays for interaction testing relies on fast, practical algorithms. Such algorithms are needed to directly construct covering arrays and variants such as covering perfect hash families. However, they are also needed for a broader class of combinatorial arrays...

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Published inSN computer science Vol. 5; no. 2; p. 247
Main Author Colbourn, Charles J.
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.02.2024
Springer Nature B.V
Subjects
Accuracy
Algorithms
Arrays
Combinatorial analysis
Combinatorial Testing and its Applications
Computer Imaging
Computer Science
Computer Systems Organization and Communication Networks
Constrictions
Construction
Data Structures and Information Theory
Efficiency
Greedy algorithms
Guarantees
Information Systems and Communication Service
Methods
Original Research
Pattern Recognition and Graphics
Software Engineering/Programming and Operating Systems
Storage
Vision
Greedy algorithm
Conditional expectation
Hash family
Covering array
Probabilistic method
Online AccessGet full text
ISSN2661-8907
2662-995X
2661-8907
DOI10.1007/s42979-023-02548-9

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Abstract The effective construction of covering arrays for interaction testing relies on fast, practical algorithms. Such algorithms are needed to directly construct covering arrays and variants such as covering perfect hash families. However, they are also needed for a broader class of combinatorial arrays defined by combinatorial restrictions, such as perfect, separating, and distributing hash families. For moderate-to-large construction problems, greedy algorithms offer fast techniques that are general and flexible. Consequently they yield the best-known explicit construction for a wide variety of array parameters. Among the greedy algorithms, one-column-at-a-time methods (such as IPO) appear to provide the most efficient techniques. For some restrictions, however, one-row-at-a-time methods guarantee the construction of an array whose size matches that of a strong probabilistic bound. Despite the practical merits of the IPO-like algorithms, this accuracy guarantee has been lacking. In this paper, a framework for greedy algorithms for a broad class of combinatorial restrictions is developed. A one-selection-at-a-time algorithm chooses the entries of the array in arbitrary order while guaranteeing to meet the probabilistic bound. It is time-efficient and uses minimal storage, but entails substantial recomputation. By storing intermediate results, the method is specialized to obtain a general one-row-at-a-time method that is faster. Finally, it is specialized to a general one-column-at-a-time and to an IPO method that consume both less time and less storage than the one-row-at-a-time approach. Crucially, each method guarantees to meet the probabilistic bound for each of the combinatorial restrictions studied.
AbstractList The effective construction of covering arrays for interaction testing relies on fast, practical algorithms. Such algorithms are needed to directly construct covering arrays and variants such as covering perfect hash families. However, they are also needed for a broader class of combinatorial arrays defined by combinatorial restrictions, such as perfect, separating, and distributing hash families. For moderate-to-large construction problems, greedy algorithms offer fast techniques that are general and flexible. Consequently they yield the best-known explicit construction for a wide variety of array parameters. Among the greedy algorithms, one-column-at-a-time methods (such as IPO) appear to provide the most efficient techniques. For some restrictions, however, one-row-at-a-time methods guarantee the construction of an array whose size matches that of a strong probabilistic bound. Despite the practical merits of the IPO-like algorithms, this accuracy guarantee has been lacking. In this paper, a framework for greedy algorithms for a broad class of combinatorial restrictions is developed. A one-selection-at-a-time algorithm chooses the entries of the array in arbitrary order while guaranteeing to meet the probabilistic bound. It is time-efficient and uses minimal storage, but entails substantial recomputation. By storing intermediate results, the method is specialized to obtain a general one-row-at-a-time method that is faster. Finally, it is specialized to a general one-column-at-a-time and to an IPO method that consume both less time and less storage than the one-row-at-a-time approach. Crucially, each method guarantees to meet the probabilistic bound for each of the combinatorial restrictions studied.
ArticleNumber 247
Author Colbourn, Charles J.
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  organization: School of Computing and Augmented Intelligence, Arizona State University
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Hash family
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Probabilistic method
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Snippet The effective construction of covering arrays for interaction testing relies on fast, practical algorithms. Such algorithms are needed to directly construct...
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springer
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StartPage 247
SubjectTerms Accuracy
Algorithms
Arrays
Combinatorial analysis
Combinatorial Testing and its Applications
Computer Imaging
Computer Science
Computer Systems Organization and Communication Networks
Constrictions
Construction
Data Structures and Information Theory
Efficiency
Greedy algorithms
Guarantees
Information Systems and Communication Service
Methods
Original Research
Pattern Recognition and Graphics
Software Engineering/Programming and Operating Systems
Storage
Vision
Title Efficient Greedy Algorithms with Accuracy Guarantees for Combinatorial Restrictions
URI https://link.springer.com/article/10.1007/s42979-023-02548-9
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