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Author

Charles J. Colbourn

Bio: Charles J. Colbourn is an academic researcher from Arizona State University. The author has contributed to research in topics: Steiner system & Combinatorial design. The author has an hindex of 51, co-authored 450 publications receiving 14887 citations. Previous affiliations of Charles J. Colbourn include University of Saskatchewan & University of York.


Papers
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BookDOI
TL;DR: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquareMutually Orthogonomic Latin Squares (MOLS)Incomplete MOLsOrthogonal ARrays of Index More Than OneOrthoghonal Array of Strength More Than TwoPairwise Balanced Designs
Abstract: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex

1,664 citations

Journal ArticleDOI
TL;DR: It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.

1,525 citations

Book
01 Jan 1987
TL;DR: The reliability polynominal Edge-disjoint subgraphs Additive and multiplicative improvements Combining the bounds The k-cycle bound Computational results References Index.
Abstract: Preliminaries Exact algorithms The computational complexity of reliability problems Exact algorithms for restricted classes The reliability polynominal Edge-disjoint subgraphs Additive and multiplicative improvements Combining the bounds The k-cycle bound Computational results References Index.

1,142 citations

Book
01 Jan 2006
TL;DR: In this paper, the authors present a design theory of small-block designs of small order for the first time in the last half of the 20th century, starting from the design of the first block designs in the early 1950s.
Abstract: PREFACE INTRODUCTION NEW! Opening the Door NEW! Design Theory: Antiquity to 1950 BLOCK DESIGNS 2-(v, k, ?) Designs of Small Order NEW! Triple Systems BIBDs with Small Block Size t-Designs with t = 3 Steiner Systems Symmetric Designs Resolvable and Near-Resolvable Designs LATIN SQUARES Latin Squares Quasigroups Mutually Orthogonal Latin Squares (MOLS) Incomplete MOLS Self-Orthogonal Latin Squares (SOLS) Orthogonal Arrays of Index More Than One Orthogonal Arrays of Strength More Than Two PAIRWISE BALANCED DESIGNS PBDs and GDDs: The Basics PBDs: Recursive Constructions PBD-Closure NEW! Group Divisible Designs PBDs, Frames, and Resolvability Pairwise Balanced Designs as Linear Spaces HADAMARD MATRICES AND RELATED DESIGNS Hadamard Matrices and Hadamard Designs Orthogonal Designs D-Optimal Matrices Bhaskar Rao Designs Generalized Hadamard Matrices Balanced Generalized Weighing Matrices and Conference Matrices Sequence Correlation Complementary, Base and Turyn Sequences NEW! Optical Orthogonal Codes OTHER COMBINATORIAL DESIGNS Association Schemes Balanced Ternary Designs Balanced Tournament Designs NEW! Bent Functions NEW! Block-Transitive Designs Complete Mappings and Sequencings of Finite Groups Configurations Correlation-Immune and Resilient Functions Costas Arrays NEW! Covering Arrays Coverings Cycle Decompositions Defining Sets NEW! Deletion-Correcting Codes Derandomization Difference Families Difference Matrices Difference Sets Difference Triangle Sets Directed Designs Factorial Designs Frequency Squares and Hypercubes Generalized Quadrangles Graph Decompositions NEW! Graph Embeddings and Designs Graphical Designs NEW! Grooming Hall Triple Systems Howell Designs NEW! Infinite Designs Linear Spaces: Geometric Aspects Lotto Designs NEW! Low Density Parity Check Codes NEW! Magic Squares Mendelsohn Designs NEW! Nested Designs Optimality and Efficiency: Comparing Block Designs Ordered Designs, Perpendicular Arrays and Permutation Sets Orthogonal Main Effect Plans Packings Partial Geometries Partially Balanced Incomplete Block Designs NEW! Perfect Hash Families NEW! Permutation Codes and Arrays NEW! Permutation Polynomials NEW! Pooling Designs NEW! Quasi-3 Designs Quasi-Symmetric Designs (r, ?)-designs Room Squares Scheduling a Tournament Secrecy and Authentication Codes Skolem and Langford Sequences Spherical Designs Starters Superimposed Codes and Combinatorial Group Testing NEW! Supersimple Designs Threshold and Ramp Schemes (t,m,s)-Nets Trades NEW! Turan Systems Tuscan Squares t-Wise Balanced Designs Whist Tournaments Youden Squares and Generalized Youden Designs RELATED MATHEMATICS Codes Finite Geometry NEW! Divisible Semiplanes Graphs and Multigraphs Factorizations of Graphs Computational Methods in Design Theory NEW! Linear Algebra and Designs Number Theory and Finite Fields Finite Groups and Designs NEW! Designs and Matroids Strongly Regular Graphs NEW! Directed Strongly Regular Graphs Two-Graphs BIBLIOGRAPHY INDEX

854 citations

Proceedings ArticleDOI
03 May 2003
TL;DR: Initial results are presented suggesting that heuristic search techniques are more effective than some of the known greedy methods for finding smaller sized test suites for software interaction testing.
Abstract: Software system faults are often caused by unexpected interactions among components. Yet the size of a test suite required to test all possible combinations of interactions can be prohibitive in even a moderately sized project. Instead, we may use pairwise or t-way testing to provide a guarantee that all pairs or t-way combinations of components are tested together This concept draws on methods used in statistical testing for manufacturing and has been extended to software system testing. A covering array, CA(N; t, k, v), is an N/spl times/k array on v symbols such that every N x t sub-array contains all ordered subsets from v symbols of size t at least once. The properties of these objects, however do not necessarily satisfy real software testing needs. Instead we examine a less studied object, the mixed level covering array and propose a new object, the variable strength covering array, which provides a more robust environment for software interaction testing. Initial results are presented suggesting that heuristic search techniques are more effective than some of the known greedy methods for finding smaller sized test suites. We present a discussion of an integrated approach for finding covering arrays and discuss how application of these techniques can be used to construct variable strength arrays.

384 citations


Cited by
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Journal Article
TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.
Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

13,333 citations

Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

7,116 citations

Journal ArticleDOI
Tamar Frankel1
TL;DR: The Essay concludes that practitioners theorize, and theorists practice, use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ.
Abstract: Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

2,077 citations

Journal ArticleDOI
TL;DR: It is shown that the STP, which subsumes the major part of Vilain and Kautz's point algebra, can be solved in polynomial time and the applicability of path consistency algorithms as preprocessing of temporal problems is studied, to demonstrate their termination and bound their complexities.

1,989 citations

Book
01 Jan 2006
TL;DR: This paper discusses Fixed-Parameter Algorithms, Parameterized Complexity Theory, and Selected Case Studies, and some of the techniques used in this work.
Abstract: PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

1,730 citations