TAPER: query-aware, partition-enhancement for large, heterogenous, graphs

Graph partitioning has long been seen as a viable approach to address Graph DBMS scalability. A partitioning, however, may introduce extra query processing latency unless it is sensitive to a specific query workload, and optimised to minimise inter-partition traversals for that workload. Additionally, it should also be possible to incrementally adjust the partitioning in reaction to changes in the graph topology, the query workload, or both. Because of their complexity, current partitioning algorithms fall short of one or both of these requirements, as they are designed for offline use and as one-off operations. The TAPER system aims to address both requirements, whilst leveraging existing partitioning algorithms. TAPER takes any given initial partitioning as a starting point, and iteratively adjusts it by swapping chosen vertices across partitions, heuristically reducing the probability of inter-partition traversals for a given pattern matching queries workload. Iterations are inexpensive thanks to time and space optimisations in the underlying support data structures. We evaluate TAPER on two different large test graphs and over realistic query workloads. Our results indicate that, given a hash-based partitioning, TAPER reduces the number of inter-partition traversals by around 80%; given an unweighted METIS partitioning, by around 30%. These reductions are achieved within 8 iterations and with the additional advantage of being workload-aware and usable online.Comment: 12 pages, 11 figures, unpublishe

Loom: Query-aware Partitioning of Online Graphs

As with general graph processing systems, partitioning data over a cluster of machines improves the scalability of graph database management systems. However, these systems will incur additional network cost during the execution of a query workload, due to inter-partition traversals. Workload-agnostic partitioning algorithms typically minimise the likelihood of any edge crossing partition boundaries. However, these partitioners are sub-optimal with respect to many workloads, especially queries, which may require more frequent traversal of specific subsets of inter-partition edges. Furthermore, they largely unsuited to operating incrementally on dynamic, growing graphs. We present a new graph partitioning algorithm, Loom, that operates on a stream of graph updates and continuously allocates the new vertices and edges to partitions, taking into account a query workload of graph pattern expressions along with their relative frequencies. First we capture the most common patterns of edge traversals which occur when executing queries. We then compare sub-graphs, which present themselves incrementally in the graph update stream, against these common patterns. Finally we attempt to allocate each match to single partitions, reducing the number of inter-partition edges within frequently traversed sub-graphs and improving average query performance. Loom is extensively evaluated over several large test graphs with realistic query workloads and various orderings of the graph updates. We demonstrate that, given a workload, our prototype produces partitionings of significantly better quality than existing streaming graph partitioning algorithms Fennel and LDG

RRR: Rank-Regret Representative

Selecting the best items in a dataset is a common task in data exploration. However, the concept of "best" lies in the eyes of the beholder: different users may consider different attributes more important, and hence arrive at different rankings. Nevertheless, one can remove "dominated" items and create a "representative" subset of the data set, comprising the "best items" in it. A Pareto-optimal representative is guaranteed to contain the best item of each possible ranking, but it can be almost as big as the full data. Representative can be found if we relax the requirement to include the best item for every possible user, and instead just limit the users' "regret". Existing work defines regret as the loss in score by limiting consideration to the representative instead of the full data set, for any chosen ranking function. However, the score is often not a meaningful number and users may not understand its absolute value. Sometimes small ranges in score can include large fractions of the data set. In contrast, users do understand the notion of rank ordering. Therefore, alternatively, we consider the position of the items in the ranked list for defining the regret and propose the {\em rank-regret representative} as the minimal subset of the data containing at least one of the top-$k$ of any possible ranking function. This problem is NP-complete. We use the geometric interpretation of items to bound their ranks on ranges of functions and to utilize combinatorial geometry notions for developing effective and efficient approximation algorithms for the problem. Experiments on real datasets demonstrate that we can efficiently find small subsets with small rank-regrets

Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on what may be broadly termed statistical data analysis. In this article, I will address fundamental aspects of this algorithmic-statistical disconnect, with an eye to bridging the gap between these two very different approaches. A concept that lies at the heart of this disconnect is that of statistical regularization, a notion that has to do with how robust is the output of an algorithm to the noise properties of the input data. Although it is nearly completely absent from computer science, which historically has taken the input data as given and modeled algorithms discretely, regularization in one form or another is central to nearly every application domain that applies algorithms to noisy data. By using several case studies, I will illustrate, both theoretically and empirically, the nonobvious fact that approximate computation, in and of itself, can implicitly lead to statistical regularization. This and other recent work suggests that, by exploiting in a more principled way the statistical properties implicit in worst-case algorithms, one can in many cases satisfy the bicriteria of having algorithms that are scalable to very large-scale databases and that also have good inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles of Database Systems (PODS 2012