We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to f...

The vendor location problem is the problem of locating a given number of vendors and determining the number of vehicles and the service zones necessary for each vendor to achieve at least a given profit. We consider two versions of the problem with different objectives: maximizing the total profit and maximizing the demand covered. The demand and profit generated by a demand point are functions...

In this paper, we present an approach for structural classification of taxonomies for knowledge acquisition from Wikipedia using standard loose frameworks. Knowledge mapped from WordNet are assigned to corresponding patterns in Wikipedia such that the syse structure are automatically acquired for related patterns and then used for knowledge generation, achievable through Learning. The paper con...

In this paper, we present an approach for structural classification of taxonomies for knowledge acquisition from Wikipedia using standard loose frameworks. Knowledge mapped from WordNet are assigned to corresponding patterns in Wikipedia such that the syse structure are automatically acquired for related patterns and then used for knowledge generation, achievable through Learning. The paper con...

Wei’s celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroids. These results are further generalized, resulting in two Wei-type duality theorems for new combinatorial structures that are introduced and named demi-matroids. These generalize matroids and are the appropriate com...

In this paper, we present an approach for structural classification of taxonomies for knowledge acquisition from Wikipedia using standard loose frameworks. Knowledge mapped from WordNet are assigned to corresponding patterns in Wikipedia such that the syse structure are automatically acquired for related patterns and then used for knowledge generation, achievable through Learning. The paper con...

Motivated by problems such as rectangle stabbing in the plane, we study the minimum hitting set and maximum independent set problems for families of d-intervals and d-union-intervals. We obtain the following: (1) constructions yielding asymptotically tight lower bounds on the integrality gaps of the associated natural linear programming relaxations; (2) an LP-relative dapproximation for the hit...