Distributed top-k aggregation queries at large

Top-k query processing is a fundamental building block for efficient ranking in a large number of applications. Efficiency is a central issue, especially for distributed settings, when the data is spread across different nodes in a network. This paper introduces novel optimization methods for top-k aggregation queries in such distributed environments. The optimizations can be applied to all algorithms that fall into the frameworks of the prior TPUT and KLEE methods. The optimizations address three degrees of freedom: 1) hierarchically grouping input lists into top-k operator trees and optimizing the tree structure, 2) computing data-adaptive scan depths for different input sources, and 3) data-adaptive sampling of a small subset of input sources in scenarios with hundreds or thousands of query-relevant network nodes. All optimizations are based on a statistical cost model that utilizes local synopses, e.g., in the form of histograms, efficiently computed convolutions, and estimators based on order statistics. The paper presents comprehensive experiments, with three different real-life datasets and using the ns-2 network simulator for a packet-level simulation of a large Internet-style network

Top-Down Induction of Decision Trees: Rigorous Guarantees and Inherent Limitations

Consider the following heuristic for building a decision tree for a function $f : \{0,1\}^n \to \{\pm 1\}$. Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the left and right subtrees respectively; terminate once the tree is an $\varepsilon$-approximation of $f$. We analyze the quality of this heuristic, obtaining near-matching upper and lower bounds: $\circ$ Upper bound: For every $f$ with decision tree size $s$ and every $\varepsilon \in (0,\frac1{2})$, this heuristic builds a decision tree of size at most $s^{O(\log(s/\varepsilon)\log(1/\varepsilon))}$. $\circ$ Lower bound: For every $\varepsilon \in (0,\frac1{2})$ and $s \le 2^{\tilde{O}(\sqrt{n})}$, there is an $f$ with decision tree size $s$ such that this heuristic builds a decision tree of size $s^{\tilde{\Omega}(\log s)}$. We also obtain upper and lower bounds for monotone functions: $s^{O(\sqrt{\log s}/\varepsilon)}$ and $s^{\tilde{\Omega}(\sqrt[4]{\log s } )}$ respectively. The lower bound disproves conjectures of Fiat and Pechyony (2004) and Lee (2009). Our upper bounds yield new algorithms for properly learning decision trees under the uniform distribution. We show that these algorithms---which are motivated by widely employed and empirically successful top-down decision tree learning heuristics such as ID3, C4.5, and CART---achieve provable guarantees that compare favorably with those of the current fastest algorithm (Ehrenfeucht and Haussler, 1989). Our lower bounds shed new light on the limitations of these heuristics. Finally, we revisit the classic work of Ehrenfeucht and Haussler. We extend it to give the first uniform-distribution proper learning algorithm that achieves polynomial sample and memory complexity, while matching its state-of-the-art quasipolynomial runtime

Stochastic Query Covering for Fast Approximate Document Retrieval

We design algorithms that, given a collection of documents and a distribution over user queries, return a small subset of the document collection in such a way that we can efficiently provide high-quality answers to user queries using only the selected subset. This approach has applications when space is a constraint or when the query-processing time increases significantly with the size of the collection. We study our algorithms through the lens of stochastic analysis and prove that even though they use only a small fraction of the entire collection, they can provide answers to most user queries, achieving a performance close to the optimal. To complement our theoretical findings, we experimentally show the versatility of our approach by considering two important cases in the context of Web search. In the first case, we favor the retrieval of documents that are relevant to the query, whereas in the second case we aim for document diversification. Both the theoretical and the experimental analysis provide strong evidence of the potential value of query covering in diverse application scenarios

Upper Bound Approximations for BlockMaxWand

BlockMaxWand is a recent advance on the Wand dynamic pruning technique, which allows efficient retrieval without any effectiveness degradation to rank K. However, while BMW uses docid-sorted indices, it relies on recording the upper bound of the term weighting model scores for each block of postings in the inverted index. Such a requirement can be disadvantageous in situations such as when an index must be updated. In this work, we examine the appropriateness of upper-bound approximation – which have previously been shown suitable for Wand– in providing efficient retrieval for BMW. Experiments on the ClueWeb12 category B13 corpus using 5000 queries from a real search engine’s query log demonstrate that BMW still provides benefits w.r.t. Wand when approximate upper bounds are used, and that, if approximations on upper bounds are tight, BMW with approximate upper bounds can provide efficiency gains w.r.t.Wand with exact upper bounds, in particular for queries of short to medium length

Measuring and Managing Answer Quality for Online Data-Intensive Services

Online data-intensive services parallelize query execution across distributed software components. Interactive response time is a priority, so online query executions return answers without waiting for slow running components to finish. However, data from these slow components could lead to better answers. We propose Ubora, an approach to measure the effect of slow running components on the quality of answers. Ubora randomly samples online queries and executes them twice. The first execution elides data from slow components and provides fast online answers; the second execution waits for all components to complete. Ubora uses memoization to speed up mature executions by replaying network messages exchanged between components. Our systems-level implementation works for a wide range of platforms, including Hadoop/Yarn, Apache Lucene, the EasyRec Recommendation Engine, and the OpenEphyra question answering system. Ubora computes answer quality much faster than competing approaches that do not use memoization. With Ubora, we show that answer quality can and should be used to guide online admission control. Our adaptive controller processed 37% more queries than a competing controller guided by the rate of timeouts.Comment: Technical Repor

VerdictDB: Universalizing Approximate Query Processing

Despite 25 years of research in academia, approximate query processing (AQP) has had little industrial adoption. One of the major causes of this slow adoption is the reluctance of traditional vendors to make radical changes to their legacy codebases, and the preoccupation of newer vendors (e.g., SQL-on-Hadoop products) with implementing standard features. Additionally, the few AQP engines that are available are each tied to a specific platform and require users to completely abandon their existing databases---an unrealistic expectation given the infancy of the AQP technology. Therefore, we argue that a universal solution is needed: a database-agnostic approximation engine that will widen the reach of this emerging technology across various platforms. Our proposal, called VerdictDB, uses a middleware architecture that requires no changes to the backend database, and thus, can work with all off-the-shelf engines. Operating at the driver-level, VerdictDB intercepts analytical queries issued to the database and rewrites them into another query that, if executed by any standard relational engine, will yield sufficient information for computing an approximate answer. VerdictDB uses the returned result set to compute an approximate answer and error estimates, which are then passed on to the user or application. However, lack of access to the query execution layer introduces significant challenges in terms of generality, correctness, and efficiency. This paper shows how VerdictDB overcomes these challenges and delivers up to 171$\times$ speedup (18.45$\times$ on average) for a variety of existing engines, such as Impala, Spark SQL, and Amazon Redshift, while incurring less than 2.6% relative error. VerdictDB is open-sourced under Apache License.Comment: Extended technical report of the paper that appeared in Proceedings of the 2018 International Conference on Management of Data, pp. 1461-1476. ACM, 201

Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k} {\epsilon} \log \frac{\epsilon N}{k})$ bits for basic counting and $O(\frac{k}{\epsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\epsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.Comment: 12 pages, to appear in the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), 201