Applications of Combinatorial Designs to Communications, Cryptography, and Networking

Colbourn, Charles J.; Dinitz, Jeffrey H.; Stinson, D. R.

doi:10.1017/cbo9780511721335.004

Cited by 105 publications

(88 citation statements)

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“…We say two such partitions P and Q are qualitatively independent if each cell of P and each cell of Q have at least one element in common. For practical reasons, we want large sets of pairwise qualitatively independent partitions [3,7,14,15].…”

Section: Set-partitionsmentioning

confidence: 99%

Multiplicity-Free Permutation Representations of the Symmetric Group

Godsil

Meagher

2010

Ann. Comb.

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Section: Set-partitionsmentioning

confidence: 99%

Multiplicity-Free Permutation Representations of the Symmetric Group

Godsil

Meagher

2010

Ann. Comb.

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“…When the finite abstract set is composed of subsets each of fixed size k, these subsets are known as blocks. Traditional instances of CDPs that involve blocks are often found in combinatorial and design theory [12], but real world problems such as tournament and conference scheduling [10], and cryptography [13], also frequently exhibit this structure. Their significance is felt acutely in real world applications such as optical network design and routing (WDM, DWDM, SONET).…”

Section: Challenging Problemsmentioning

confidence: 99%

“…see [13] for a survey). They deal essentially with the search for families of sets with certain properties subject to constraints including intersection and cardinality restrictions.…”

Section: Introductionmentioning

confidence: 99%

Enhancing set constraint solvers with lexicographic bounds

Sadler

Gervet

2007

J Heuristics

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Abstract. Since their beginning in constraint programming, set solvers have been applied to a wide range of combinatorial search problems, such as bin-packing, set partitioning, circuit design, and Combinatorial Design Problems. In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to the challenging symmetrical set problems often cast as Combinatorial Design Problems (CDPs). While CDPs find a natural formulation in the language of sets, in constraint programming literature, alternative models are often used due to a lack of efficiency of traditional FS solvers. We first identify the main structural components of CDPs that render their modeling suitable to set languages but their solving a technical challenge. Our new prototype solver extends the traditional subset variable domain with lexicographic bounds that better approximate a set domain by satisfying the cardinality restrictions applied to the variable, and allow for active symmetry breaking using ordering constraints. Our contribution includes the formal and practical framework of the new solver implemented on top of a traditional set solver, and an empirical evaluation on benchmark CDPs.

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“…Several researchers have studied combinatorial group testing and its applications to cryptography and information encoding (e.g., see [16,26]). This area is directed at performing group tests on subsets of a given set S to identify defective elements in S. The area has not to date been applied to data index integrity, but in this paper we show an interesting connection between data forensics marking and a new reduced-randomness construction of a nonadaptive combinatorial group testing scheme, which may be of independent interest.…”

Section: Introductionmentioning

confidence: 99%

Indexing Information for Data Forensics

Goodrich

Atallah

Tamassia

2005

Lecture Notes in Computer Science

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Abstract. We introduce novel techniques for organizing the indexing structures of how data is stored so that alterations from an original version can be detected and the changed values specifically identified. We give forensic constructions for several fundamental data structures, including arrays, linked lists, binary search trees, skip lists, and hash tables. Some of our constructions are based on a new reduced-randomness construction for nonadaptive combinatorial group testing.

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Applications of Combinatorial Designs to Communications, Cryptography, and Networking

Cited by 105 publications

References 0 publications

Multiplicity-Free Permutation Representations of the Symmetric Group

Multiplicity-Free Permutation Representations of the Symmetric Group

Enhancing set constraint solvers with lexicographic bounds

Indexing Information for Data Forensics

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