A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.Comment: PASC '18, Code: https://github.com/ligmg/ligm

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

MapReduce is Good Enough? If All You Have is a Hammer, Throw Away Everything That's Not a Nail!

Hadoop is currently the large-scale data analysis "hammer" of choice, but there exist classes of algorithms that aren't "nails", in the sense that they are not particularly amenable to the MapReduce programming model. To address this, researchers have proposed MapReduce extensions or alternative programming models in which these algorithms can be elegantly expressed. This essay espouses a very different position: that MapReduce is "good enough", and that instead of trying to invent screwdrivers, we should simply get rid of everything that's not a nail. To be more specific, much discussion in the literature surrounds the fact that iterative algorithms are a poor fit for MapReduce: the simple solution is to find alternative non-iterative algorithms that solve the same problem. This essay captures my personal experiences as an academic researcher as well as a software engineer in a "real-world" production analytics environment. From this combined perspective I reflect on the current state and future of "big data" research