Mahmoud Abo Khamis

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We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on computing joins. In addition, we use our framework and the same algorithm to show a series of what are colloquially known as(More)
Recently, Gottlob, Lee, Valiant, and Valiant (GLVV) presented an output size bound for join queries with functional dependencies (FD), based on a linear program on polymatroids. GLVV bound strictly generalizes the bound of Atserias, Grohe and Marx (AGM) for queries with no FD, in which case there are known algorithms running within the AGM-bound and thus(More)
Recent works on bounding the output size of a conjunctive query with functional dependencies and degree bounds have shown a deep connection between fundamental questions in information theory and database theory. We prove analogous output bounds for <i>disjunctive datalog rules</i>, and answer several open questions regarding the tightness and looseness of(More)
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and present the first combinatorial results on the output list size. These generalize and enhance some of the existing(More)
We introduce a unified framework for a class of optimization based statistical learning problems used by LogicBlox retail-planning and forecasting applications, where the input data is given by queries over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. The(More)
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