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Randomization is a common feature of everyday resource allocation. We generalize the theory of randomized assignment to accommodate various real-world constraints such as group-specific quotas (" controlled choice ") in school choice and house allocation, and scheduling and curriculum constraints in course allocation. We develop new mechanisms that are ex(More)
In sports timetabling, finding feasible pattern sets for a round robin tournament is a significant problem. Although this problem has been tackled in several ways, good characterization of feasible pattern sets is not known yet. In this paper, we consider the feasibility of a pattern set, and propose a necessary condition for feasible pattern sets. In the(More)
Consider two orthogonal closed chains on a cylinder. These chains are monotone with respect to the tangential Θ direction. We wish to rigidly move one chain so that the total area between the two is minimized. This minimization is a geometric measure of similarity between two melodies proposed by´O Maidín. The Θ direction represents time and the axial(More)
Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is dened on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4d2k= p 3e) time where n denotes the number of vertices.(More)
The Traveling Tournament Problem is a complex combinatorial optimization problem in tournament timetabling, which asks a schedule of home/away games meeting specific feasibility requirements , while also minimizing the total distance traveled by all the n teams (n is even). Despite intensive algorithmic research on this problem over the last decade, most(More)
The literature on random mechanisms often describes outcomes incompletely as random assignments expressing the expected number of objects of each type assigned to dierent agents and a set of feasibility constraints that a pure assignment must satisfy. We provide a necessary and sucient condition (the bihierarchy condition) for the set of constraints to have(More)