Holroyd and Propp used Hall’s marriage theorem to show that, given a probability distribution π on a finite set S, there exists an infinite sequence s1, s2, . . . in S such that for all integers k ≥ 1 and all s in S, the number of i in [1, k] with si = s differs from k π(s) by at most 1. We prove a generalization of this result using a simple explicit algorithm. A special case of this algorithm...

The discrepancy function of a point distribution measures the deviation from the uniform distribution. Different versions of the discrepancy function capture this deviation with respect to different geometric objects. Via Koksma-Hlawka inequalities the norm of the discrepancy function in a function space is intimately connected to the worst case integration error of the quasi-Monte Carlo integr...

Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative rounding. We provide an extension of the discrepancy-based rounding algorithm due to Lovett-Meka that (i) combines the advantages of both randomized and iterat...

Discrepancy theory addresses the general issue of approximating one measure by another one. Originally an offshoot of diophantine approximation theory [34], the area has expanded into applied mathematics, and now, computer science. Besides providing the theoretical foundation for sampling, it holds some of the keys to understanding the computational power of randomization. Here are a few applic...