Combinatorial Characterizations of K-matrices

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.Comment: 17 pages; v2, v3: clarified proof of Thm 5.5, minor correction

Faster truncated integer multiplication

We present new algorithms for computing the low n bits or the high n bits of the product of two n-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full 2n-bit product, assuming that the underlying integer multiplication algorithm relies on computing cyclic convolutions of real sequences.Comment: 28 page

An extension of SPARQL for expressing qualitative preferences

In this paper we present SPREFQL, an extension of the SPARQL language that allows appending a PREFER clause that expresses "soft" preferences over the query results obtained by the main body of the query. The extension does not add expressivity and any SPREFQL query can be transformed to an equivalent standard SPARQL query. However, clearly separating preferences from the "hard" patterns and filters in the WHERE clause gives queries where the intention of the client is more cleanly expressed, an advantage for both human readability and machine optimization. In the paper we formally define the syntax and the semantics of the extension and we also provide empirical evidence that optimizations specific to SPREFQL improve run-time efficiency by comparison to the usually applied optimizations on the equivalent standard SPARQL query.Comment: Accepted to the 2017 International Semantic Web Conference, Vienna, October 201

Solving Functional Constraints by Variable Substitution

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints