1,877 research outputs found

    CLUDE: An Efficient Algorithm for LU Decomposition Over a Sequence of Evolving Graphs

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    Session: Matrix Factorization, Clustering and Probabilistic DataIn many applications, entities and their relationships are represented by graphs. Examples include the WWW (web pages and hyperlinks) and bibliographic networks (authors and co-authorship). A graph can be conveniently modeled by a matrix from which various quantitative measures are derived. Some example measures include PageRank and SALSA (which measure nodes’ importance), and Personalized PageRank and Random Walk with Restart (which measure proximities between nodes). To compute these measures, linear systems of the form Ax = b, where A is a matrix that captures a graph’s structure, need to be solved. To facilitate solving the linear system, the matrix A is often decomposed into two triangular matrices (L and U). In a dynamic world, the graph that models it changes with time and thus is the matrix A that represents the graph. We consider a sequence of evolving graphs and its associated sequence of evolving matrices. We study how LU-decomposition should be done over the sequence so that (1) the decomposition is efficient and (2) the resulting LU matrices best preserve the sparsity of the matrices A’s (i.e., the number of extra non-zero entries introduced in L and U are minimized.) We propose a cluster-based algorithm CLUDE for solving the problem. Through an experimental study, we show that CLUDE is about an order of magnitude faster than the traditional incremental update algorithm. The number of extra non-zero entries introduced by CLUDE is also about an order of magnitude fewer than that of the traditional algorithm. CLUDE is thus an efficient algorithm for LU decomposition that produces high-quality LU matrices over an evolving matrix sequence.published_or_final_versio

    A Closer Look at Lightweight Graph Reordering

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    Graph analytics power a range of applications in areas as diverse as finance, networking and business logistics. A common property of graphs used in the domain of graph analytics is a power-law distribution of vertex connectivity, wherein a small number of vertices are responsible for a high fraction of all connections in the graph. These richly-connected (hot) vertices inherently exhibit high reuse. However, their sparse distribution in memory leads to a severe underutilization of on-chip cache capacity. Prior works have proposed lightweight skew-aware vertex reordering that places hot vertices adjacent to each other in memory, reducing the cache footprint of hot vertices. However, in doing so, they may inadvertently destroy the inherent community structure within the graph, which may negate the performance gains achieved from the reduced footprint of hot vertices. In this work, we study existing reordering techniques and demonstrate the inherent tension between reducing the cache footprint of hot vertices and preserving original graph structure. We quantify the potential performance loss due to disruption in graph structure for different graph datasets. We further show that reordering techniques that employ fine-grain reordering significantly increase misses in the higher level caches, even when they reduce misses in the last-level cache. To overcome the limitations of existing reordering techniques, we propose Degree-Based Grouping (DBG), a novel lightweight reordering technique that employs a coarse-grain reordering to largely preserve graph structure while reducing the cache footprint of hot vertices. Our evaluation on 40 combinations of various graph applications and datasets shows that, compared to a baseline with no reordering, DBG yields an average application speed-up of 16.8% vs 11.6% for the best-performing existing lightweight technique.Comment: Fixed ill-formatted page 6 from the earlier version. No content change

    Datacenter Traffic Control: Understanding Techniques and Trade-offs

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    Datacenters provide cost-effective and flexible access to scalable compute and storage resources necessary for today's cloud computing needs. A typical datacenter is made up of thousands of servers connected with a large network and usually managed by one operator. To provide quality access to the variety of applications and services hosted on datacenters and maximize performance, it deems necessary to use datacenter networks effectively and efficiently. Datacenter traffic is often a mix of several classes with different priorities and requirements. This includes user-generated interactive traffic, traffic with deadlines, and long-running traffic. To this end, custom transport protocols and traffic management techniques have been developed to improve datacenter network performance. In this tutorial paper, we review the general architecture of datacenter networks, various topologies proposed for them, their traffic properties, general traffic control challenges in datacenters and general traffic control objectives. The purpose of this paper is to bring out the important characteristics of traffic control in datacenters and not to survey all existing solutions (as it is virtually impossible due to massive body of existing research). We hope to provide readers with a wide range of options and factors while considering a variety of traffic control mechanisms. We discuss various characteristics of datacenter traffic control including management schemes, transmission control, traffic shaping, prioritization, load balancing, multipathing, and traffic scheduling. Next, we point to several open challenges as well as new and interesting networking paradigms. At the end of this paper, we briefly review inter-datacenter networks that connect geographically dispersed datacenters which have been receiving increasing attention recently and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial

    Efficient Diversification of Web Search Results

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    In this paper we analyze the efficiency of various search results diversification methods. While efficacy of diversification approaches has been deeply investigated in the past, response time and scalability issues have been rarely addressed. A unified framework for studying performance and feasibility of result diversification solutions is thus proposed. First we define a new methodology for detecting when, and how, query results need to be diversified. To this purpose, we rely on the concept of "query refinement" to estimate the probability of a query to be ambiguous. Then, relying on this novel ambiguity detection method, we deploy and compare on a standard test set, three different diversification methods: IASelect, xQuAD, and OptSelect. While the first two are recent state-of-the-art proposals, the latter is an original algorithm introduced in this paper. We evaluate both the efficiency and the effectiveness of our approach against its competitors by using the standard TREC Web diversification track testbed. Results shown that OptSelect is able to run two orders of magnitude faster than the two other state-of-the-art approaches and to obtain comparable figures in diversification effectiveness.Comment: VLDB201

    LongLLMLingua: Accelerating and Enhancing LLMs in Long Context Scenarios via Prompt Compression

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    In long context scenarios, large language models (LLMs) face three main challenges: higher computational/financial cost, longer latency, and inferior performance. Some studies reveal that the performance of LLMs depends on both the density and the position of the key information (question relevant) in the input prompt. Inspired by these findings, we propose LongLLMLingua for prompt compression towards improving LLMs' perception of the key information to simultaneously address the three challenges. We conduct evaluation on a wide range of long context scenarios including single-/multi-document QA, few-shot learning, summarization, synthetic tasks, and code completion. The experimental results show that LongLLMLingua compressed prompt can derive higher performance with much less cost. The latency of the end-to-end system is also reduced. For example, on NaturalQuestions benchmark, LongLLMLingua gains a performance boost of up to 17.1% over the original prompt with ~4x fewer tokens as input to GPT-3.5-Turbo. It can derive cost savings of \$28.5 and \$27.4 per 1,000 samples from the LongBench and ZeroScrolls benchmark, respectively. Additionally, when compressing prompts of ~10k tokens at a compression rate of 2x-10x, LongLLMLingua can speed up the end-to-end latency by 1.4x-3.8x. Our code is available at https://aka.ms/LLMLingua

    Database Optimization Aspects for Information Retrieval

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    There is a growing need for systems that can process queries, combining both structured data and text. One way to provide such functionality is to integrate information retrieval (IR) techniques in a database management system (DBMS). However, both IR and database research have been separate research fields for decades, resulting in different - even conflicting - approaches to data management. Each DBMS has a component called a "query optimizer", which plays a crucial role in the efficiency and flexibility of the system. So, for successful integration the IR techniques and data structures, as well as the DBMS query optimizer, should be adapted to enable mutual cooperation. The author concentrates on top-N queries - a common class of IR queries. An IR top-N query asks for the N best documents given a set of keywords. The author proposes processing the data in batches as a compromise between IR and DBMS query processing. Experiments with this technique show that porting IR optimization techniques is (still) not a promising option due to the additional administrative overhead. Two new mathematical models are introduced to eliminate this overhead: a model that predicts selectivity, which is a crucial factor in the execution costs, and a model that predicts the quality of the top-N
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