A first course in discrete structures with applications to computer science

We introduce the Multi-Structural Database, a new data framework to support efficient analysis of large, complex data sets. An instance of the model consists of a set of data objects, together with a schema that specifies segmentations of the set of data objects according to multiple distinct criteria (e.g., into a taxonomy based on a hierarchical attribute). Within this model, we develop a rich set of analytical operations and design highly efficient algorithms for these operations. Our operations are formulated as optimization problems, and allow the user to analyze the underlying data in terms of the allowed segmentations.

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“…, d if and only if it contains x, i for all i. This lattice is sometimes called the direct product of the dimensional lattices [27].…”

Section: Msdbmentioning

confidence: 99%

Multi-structural databases

Fagin

Guha

Kumar

et al. 2005

Proceedings of the Twenty-Fourth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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“…Furthermore, observe that the shape tuple of a MATLAB expression can be any element in some equivalence class under ℘. Each equivalence class in the set of equivalence classes under ℘-called the quotient set of S by ℘ (see [14])-corresponds to a canonical shape tuple and vice versa.…”

Section: Shape Algebra Basicsmentioning

confidence: 99%

Computing Array Shapes in MATLAB

Joisha¹,

Shenoy²,

Banerjee³

2003

Languages and Compilers for Parallel Computing

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Abstract. This paper deals with the problem of statically inferring the shape of an array in languages such as MATLAB. Inferring an array's shape is desirable because it empowers better compilation and interpretation; specifically, knowing an array's shape could permit reductions in the number of run-time array conformability checks, enable memory preallocation optimizations, and facilitate the in-lining of "scalarized" code. This paper describes how the shape of a MATLAB expression can be determined statically, based on a methodology of systematic matrix formulations. The approach capitalizes on the algebraic properties that underlie MATLAB's shape semantics and exactly captures the shape that the MATLAB expression assumes at run time. Some of the highlights of the approach are its applicability to a large class of MATLAB functions and its uniformity. Our methods are compared with the previous shadow variable scheme, and we show how the algebraic view allows inferences not deduced by the traditional approach.

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“…Moreover, the dual of a read-k-CNF is a read-k-DNF, and vice-versa. By the duality law (e.g., Tremblay & Manohar, 1961), any identity or theorem about formulas remains true when the formulas are replaced by their duals.…”

Section: Dualitymentioning

confidence: 99%

Untitled

1999

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Abstract. We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("read-k" monotone CNF). Let f : {0, 1} n → {0, 1} be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f . The algorithm's only method of obtaining information about f is through membership queries, i.e., by inquiring about the value f (x) for points x ∈ {0, 1} n . The algorithm yields an incremental polynomial output time solution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.

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A first course in discrete structures with applications to computer science

Abstract: This paper describes an introductory course in discrete structures for the undergraduate computer science student that has evolved at the University of Saskatchewan, Saskatoon. The philosophy of suth a course and certain problems encountered in preparing and teaching it are discussed.

Cited by 48 publications

References 5 publications

Multi-structural databases

Multi-structural databases

Computing Array Shapes in MATLAB

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