Settling the Sample Complexity of Single-parameter Revenue Maximization

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an $\epsilon$-net of the mechanism space, explicitly or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. Our lower bounds are also unified under a meta construction of hard instances.Comment: 49 pages, Accepted by STOC1

Simple Load Balancing for Distributed Hash Tables

Distributed hash tables have recently become a useful building block for a variety of distributed applications. However, current schemes based upon consistent hashing require both considerable implementation complexity and substantial storage overhead to achieve desired load balancing goals. We argue in this paper that these goals can b e achieved more simply and more cost-effectively. First, we suggest the direct application of the "power of two choices" paradigm, whereby an item is stored at the less loaded of two (or more) random alternatives. We then consider how associating a small constant number of hash values with a key can naturally b e extended to support other load balancing methods, including load-stealing or load-shedding schemes, as well as providing natural fault-tolerance mechanisms

A simple proof for visibility paths in simple polygons

The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths