MADlib is a free, open-source library of in-database analytic methods. It provides an evolving suite of SQL-based algorithms for machine learning, data mining and statistics that run at scale within a database engine, with no need for data import/export to other tools. The goal is for MADlib to eventually serve a role for scalable database systems that is similar to the CRAN library for R: a community repository of statistical methods, this time written with scale and parallelism in mind. In this paper we introduce the MADlib project, including the background that led to its beginnings, and the motivation for its open-source nature. We provide an overview of the library's architecture and design patterns, and provide a description of various statistical methods in that context. We include performance and speedup results of a core design pattern from one of those methods over the Greenplum parallel DBMS on a modest-sized test cluster. We then report on two initial efforts at incorporating academic research into MADlib, which is one of the project's goals. MADlib is freely available at http://madlib.net, and the project is open for contributions of both new methods, and ports to additional database platforms.

We resolve the worst-case price of anarchy (POA) of atomic splittable congestion games. Prior to this work, no tight bounds on the POA in such games were known, even for the simplest non-trivial special case of affine cost functions. We make two distinct contributions. On the upper-bound side, we define the framework of “local smoothness”, which refines the standard smoothness framework for games with convex strategy sets. While standard smoothness arguments cannot establish tight bounds on the POA in atomic splittable congestion games, we prove that local smoothness arguments can. Further, we prove that every POA bound derived via local smoothness applies automatically to every correlated equilibrium of the game. Unlike standard smoothness arguments, bounds proved using local smoothness do not always apply to the coarse correlated equilibria of the game. Our second contribution is a very general lower bound: for every set ℒ that satisfies mild technical conditions, the worst-case POA of pure Nash equilibria in atomic splittable congestion games with cost functions in ℒ is exactly the smallest upper bound provable using local smoothness arguments. In particular, the worst-case POA of pure Nash equilibria, mixed Nash equilibria, and correlated equilibria coincide in such games.

We show exact values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients. The given values also hold for weighted and unweighted network congestion games.