Showing papers by "Google published in 2008"

MapReduce: simplified data processing on large clusters

Abstract: MapReduce is a programming model and an associated implementation for processing and generating large datasets that is amenable to a broad variety of real-world tasks. Users specify the computation in terms of a map and a reduce function, and the underlying runtime system automatically parallelizes the computation across large-scale clusters of machines, handles machine failures, and schedules inter-machine communication to make efficient use of the network and disks. Programmers find the system easy to use: more than ten thousand distinct MapReduce programs have been implemented internally at Google over the past four years, and an average of one hundred thousand MapReduce jobs are executed on Google's clusters every day, processing a total of more than twenty petabytes of data per day.

Introduction to Information Retrieval

Abstract: Class-tested and coherent, this groundbreaking new textbook teaches web-era information retrieval, including web search and the related areas of text classification and text clustering from basic concepts. Written from a computer science perspective by three leading experts in the field, it gives an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections. All the important ideas are explained using examples and figures, making it perfect for introductory courses in information retrieval for advanced undergraduates and graduate students in computer science. Based on feedback from extensive classroom experience, the book has been carefully structured in order to make teaching more natural and effective. Although originally designed as the primary text for a graduate or advanced undergraduate course in information retrieval, the book will also create a buzz for researchers and professionals alike.

Bigtable: A Distributed Storage System for Structured Data

Abstract: Bigtable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in Bigtable, including web indexing, Google Earth, and Google Finance. These applications place very different demands on Bigtable, both in terms of data size (from URLs to web pages to satellite imagery) and latency requirements (from backend bulk processing to real-time data serving). Despite these varied demands, Bigtable has successfully provided a flexible, high-performance solution for all of these Google products. In this article, we describe the simple data model provided by Bigtable, which gives clients dynamic control over data layout and format, and we describe the design and implementation of Bigtable.

The Datacenter as a Computer: An Introduction to the Design of Warehouse-Scale Machines

Abstract: As computation continues to move into the cloud, the computing platform of interest no longer resembles a pizza box or a refrigerator, but a warehouse full of computers. These new large datacenters are quite different from traditional hosting facilities of earlier times and cannot be viewed simply as a collection of co-located servers. Large portions of the hardware and software resources in these facilities must work in concert to efficiently deliver good levels of Internet service performance, something that can only be achieved by a holistic approach to their design and deployment. In other words, we must treat the datacenter itself as one massive warehouse-scale computer (WSC). We describe the architecture of WSCs, the main factors influencing their design, operation, and cost structure, and the characteristics of their software base. We hope it will be useful to architects and programmers of today's WSCs, as well as those of future many-core platforms which may one day implement the equivalent of today's WSCs on a single board. Table of Contents: Introduction / Workloads and Software Infrastructure / Hardware Building Blocks / Datacenter Basics / Energy and Power Efficiency / Modeling Costs / Dealing with Failures and Repairs / Closing Remarks

Efficient projections onto the l1-ball for learning in high dimensions

Abstract: We describe efficient algorithms for projecting a vector onto the l1-ball. We present two methods for projection. The first performs exact projection in O(n) expected time, where n is the dimension of the space. The second works on vectors k of whose elements are perturbed outside the l1-ball, projecting in O(k log(n)) time. This setting is especially useful for online learning in sparse feature spaces such as text categorization applications. We demonstrate the merits and effectiveness of our algorithms in numerous batch and online learning tasks. We show that variants of stochastic gradient projection methods augmented with our efficient projection procedures outperform interior point methods, which are considered state-of-the-art optimization techniques. We also show that in online settings gradient updates with l1 projections outperform the exponentiated gradient algorithm while obtaining models with high degrees of sparsity.

Amdahl's Law in the Multicore Era

Abstract: Augmenting Amdahl's law with a corollary for multicore hardware makes it relevant to future generations of chips with multiple processor cores. Obtaining optimal multicore performance will require further research in both extracting more parallelism and making sequential cores faster.

Beyond sliding windows: Object localization by efficient subwindow search

Abstract: Most successful object recognition systems rely on binary classification, deciding only if an object is present or not, but not providing information on the actual object location. To perform localization, one can take a sliding window approach, but this strongly increases the computational cost, because the classifier function has to be evaluated over a large set of candidate subwindows. In this paper, we propose a simple yet powerful branch-and-bound scheme that allows efficient maximization of a large class of classifier functions over all possible subimages. It converges to a globally optimal solution typically in sublinear time. We show how our method is applicable to different object detection and retrieval scenarios. The achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task, such as SVMs with a spatial pyramid kernel or nearest neighbor classifiers based on the chi2-distance. We demonstrate state-of-the-art performance of the resulting systems on the UIUC Cars dataset, the PASCAL VOC 2006 dataset and in the PASCAL VOC 2007 competition.

Aggregating inconsistent information: Ranking and clustering

Abstract: We address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs. Specifically, the problems we address are rank aggregation, the feedback arc set problem on tournaments, and correlation and consensus clustering. We show that for all these problems (and various weighted versions of them), we can obtain improved approximation factors using essentially the same remarkably simple algorithm. Additionally, we almost settle a long-standing conjecture of Bang-Jensen and Thomassen and show that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.

Modeling Online Reviews with Multi-grain Topic Models

Abstract: In this paper we present a novel framework for extracting the ratable aspects of objects from online user reviews. Extracting such aspects is an important challenge in automatically mining product opinions from the web and in generating opinion-based summaries of user reviews. Our models are based on extensions to standard topic modeling methods such as LDA and PLSA to induce multi-grain topics. We argue that multi-grain models are more appropriate for our task since standard models tend to produce topics that correspond to global properties of objects (e.g., the brand of a product type) rather than the aspects of an object that tend to be rated by a user. The models we present not only extract ratable aspects, but also cluster them into coherent topics, e.g., `waitress' and `bartender' are part of the same topic `staff' for restaurants. This differentiates it from much of the previous work which extracts aspects through term frequency analysis with minimal clustering. We evaluate the multi-grain models both qualitatively and quantitatively to show that they improve significantly upon standard topic models.

WebTables: exploring the power of tables on the web

Abstract: The World-Wide Web consists of a huge number of unstructured documents, but it also contains structured data in the form of HTML tables. We extracted 14.1 billion HTML tables from Google's general-purpose web crawl, and used statistical classification techniques to find the estimated 154M that contain high-quality relational data. Because each relational table has its own "schema" of labeled and typed columns, each such table can be considered a small structured database. The resulting corpus of databases is larger than any other corpus we are aware of, by at least five orders of magnitude.We describe the WEBTABLES system to explore two fundamental questions about this collection of databases. First, what are effective techniques for searching for structured data at search-engine scales? Second, what additional power can be derived by analyzing such a huge corpus?First, we develop new techniques for keyword search over a corpus of tables, and show that they can achieve substantially higher relevance than solutions based on a traditional search engine. Second, we introduce a new object derived from the database corpus: the attribute correlation statistics database (AcsDB) that records corpus-wide statistics on co-occurrences of schema elements. In addition to improving search relevance, the AcsDB makes possible several novel applications: schema auto-complete, which helps a database designer to choose schema elements; attribute synonym finding, which automatically computes attribute synonym pairs for schema matching; and join-graph traversal, which allows a user to navigate between extracted schemas using automatically-generated join links.

A Joint Model of Text and Aspect Ratings for Sentiment Summarization

Abstract: Online reviews are often accompanied with numerical ratings provided by users for a set of service or product aspects. We propose a statistical model which is able to discover corresponding topics in text and extract textual evidence from reviews supporting each of these aspect ratings ‐ a fundamental problem in aspect-based sentiment summarization (Hu and Liu, 2004a). Our model achieves high accuracy, without any explicitly labeled data except the user provided opinion ratings. The proposed approach is general and can be used for segmentation in other applications where sequential data is accompanied with correlated signals.

Modeling online reviews with multi-grain topic models

Abstract: In this paper we present a novel framework for extracting the ratable aspects of objects from online user reviews. Extracting such aspects is an important challenge in automatically mining product opinions from the web and in generating opinion-based summaries of user reviews [18, 19, 7, 12, 27, 36, 21]. Our models are based on extensions to standard topic modeling methods such as LDA and PLSA to induce multi-grain topics. We argue that multi-grain models are more appropriate for our task since standard models tend to produce topics that correspond to global properties of objects (e.g., the brand of a product type) rather than the aspects of an object that tend to be rated by a user. The models we present not only extract ratable aspects, but also cluster them into coherent topics, e.g., 'waitress' and 'bartender' are part of the same topic 'staff' for restaurants. This differentiates it from much of the previous work which extracts aspects through term frequency analysis with minimal clustering. We evaluate the multi-grain models both qualitatively and quantitatively to show that they improve significantly upon standard topic models.

Technology-Driven, Highly-Scalable Dragonfly Topology

Abstract: Evolving technology and increasing pin-bandwidth motivate the use of high-radix routers to reduce the diameter, latency, and cost of interconnection networks. High-radix networks, however, require longer cables than their low-radix counterparts. Because cables dominate network cost, the number of cables, and particularly the number of long, global cables should be minimized to realize an efficient network. In this paper, we introduce the dragonfly topology which uses a group of high-radix routers as a virtual router to increase the effective radix of the network. With this organization, each minimally routed packet traverses at most one global channel. By reducing global channels, a dragonfly reduces cost by 20% compared to a flattened butterfly and by 52% compared to a folded Clos network in configurations with ≥ 16K nodes.We also introduce two new variants of global adaptive routing that enable load-balanced routing in the dragonfly. Each router in a dragonfly must make an adaptive routing decision based on the state of a global channel connected to a different router. Because of the indirect nature of this routing decision, conventional adaptive routing algorithms give degraded performance. We introduce the use of selective virtual-channel discrimination and the use of credit round-trip latency to both sense and signal channel congestion. The combination of these two methods gives throughput and latency that approaches that of an ideal adaptive routing algorithm.

All your iFRAMEs point to Us

Abstract: As the web continues to play an ever increasing role in information exchange, so too is it becoming the prevailing platform for infecting vulnerable hosts. In this paper, we provide a detailed study of the pervasiveness of so-called drive-by downloads on the Internet. Drive-by downloads are caused by URLs that attempt to exploit their visitors and cause malware to be installed and run automatically. Over a period of 10 months we processed billions of URLs, and our results shows that a non-trivial amount, of over 3 million malicious URLs, initiate drive-by downloads. An even more troubling finding is that approximately 1.3% of the incoming search queries to Google's search engine returned at least one URL labeled as malicious in the results page. We also explore several aspects of the drive-by downloads problem. Specifically, we study the relationship between the user browsing habits and exposure to malware, the techniques used to lure the user into the malware distribution networks, and the different properties of these networks.

Video suggestion and discovery for youtube: taking random walks through the view graph

Abstract: The rapid growth of the number of videos in YouTube provides enormous potential for users to find content of interest to them. Unfortunately, given the difficulty of searching videos, the size of the video repository also makes the discovery of new content a daunting task. In this paper, we present a novel method based upon the analysis of the entire user-video graph to provide personalized video suggestions for users. The resulting algorithm, termed Adsorption, provides a simple method to efficiently propagate preference information through a variety of graphs. We extensively test the results of the recommendations on a three month snapshot of live data from YouTube.

VisualRank: Applying PageRank to Large-Scale Image Search

Abstract: Because of the relative ease in understanding and processing text, commercial image-search systems often rely on techniques that are largely indistinguishable from text search. Recently, academic studies have demonstrated the effectiveness of employing image-based features to provide either alternative or additional signals to use in this process. However, it remains uncertain whether such techniques will generalize to a large number of popular Web queries and whether the potential improvement to search quality warrants the additional computational cost. In this work, we cast the image-ranking problem into the task of identifying "authority" nodes on an inferred visual similarity graph and propose VisualRank to analyze the visual link structures among images. The images found to be "authorities" are chosen as those that answer the image-queries well. To understand the performance of such an approach in a real system, we conducted a series of large-scale experiments based on the task of retrieving images for 2,000 of the most popular products queries. Our experimental results show significant improvement, in terms of user satisfaction and relevancy, in comparison to the most recent Google image search results. Maintaining modest computational cost is vital to ensuring that this procedure can be used in practice; we describe the techniques required to make this system practical for large-scale deployment in commercial search engines.

Using Static Analysis to Find Bugs

Abstract: Static analysis examines code in the absence of input data and without running the code. It can detect potential security violations (SQL injection), runtime errors (dereferencing a null pointer) and logical inconsistencies (a conditional test that can't possibly be true). Although a rich body of literature exists on algorithms and analytical frameworks used by such tools, reports describing experiences in industry are much harder to come by. The authors describe FindBugs, an open source static-analysis tool for Java, and experiences using it in production settings. FindBugs evaluates what kinds of defects can be effectively detected with relatively simple techniques and helps developers understand how to incorporate such tools into software development.

Face tracking and recognition with visual constraints in real-world videos

Abstract: We address the problem of tracking and recognizing faces in real-world, noisy videos. We track faces using a tracker that adaptively builds a target model reflecting changes in appearance, typical of a video setting. However, adaptive appearance trackers often suffer from drift, a gradual adaptation of the tracker to non-targets. To alleviate this problem, our tracker introduces visual constraints using a combination of generative and discriminative models in a particle filtering framework. The generative term conforms the particles to the space of generic face poses while the discriminative one ensures rejection of poorly aligned targets. This leads to a tracker that significantly improves robustness against abrupt appearance changes and occlusions, critical for the subsequent recognition phase. Identity of the tracked subject is established by fusing pose-discriminant and person-discriminant features over the duration of a video sequence. This leads to a robust video-based face recognizer with state-of-the-art recognition performance. We test the quality of tracking and face recognition on real-world noisy videos from YouTube as well as the standard Honda/UCSD database. Our approach produces successful face tracking results on over 80% of all videos without video or person-specific parameter tuning. The good tracking performance induces similarly high recognition rates: 100% on Honda/UCSD and over 70% on the YouTube set containing 35 celebrities in 1500 sequences.

A New Baseline for Image Annotation

Abstract: Automatically assigning keywords to images is of great interest as it allows one to index, retrieve, and understand large collections of image data. Many techniques have been proposed for image annotation in the last decade that give reasonable performance on standard datasets. However, most of these works fail to compare their methods with simple baseline techniques to justify the need for complex models and subsequent training. In this work, we introduce a new baseline technique for image annotation that treats annotation as a retrieval problem. The proposed technique utilizes low-level image features and a simple combination of basic distances to find nearest neighbors of a given image. The keywords are then assigned using a greedy label transfer mechanism. The proposed baseline outperforms the current state-of-the-art methods on two standard and one large Web dataset. We believe that such a baseline measure will provide a strong platform to compare and better understand future annotation techniques.

Pfp: parallel fp-growth for query recommendation

Abstract: Frequent itemset mining (FIM) is a useful tool for discovering frequently co-occurrent items. Since its inception, a number of significant FIM algorithms have been developed to speed up mining performance. Unfortunately, when the dataset size is huge, both the memory use and computational cost can still be prohibitively expensive. In this work, we propose to parallelize the FP-Growth algorithm (we call our parallel algorithm PFP) on distributed machines. PFP partitions computation in such a way that each machine executes an independent group of mining tasks. Such partitioning eliminates computational dependencies between machines, and thereby communication between them. Through empirical study on a large dataset of 802,939 Web pages and 1,021,107 tags, we demonstrate that PFP can achieve virtually linear speedup. Besides scalability, the empirical study demonstrates that PFP to be promising for supporting query recommendation for search engines.

Building a Sentiment Summarizer for Local Service Reviews

Abstract: Online user reviews are increasingly becoming the de-facto standard for measuring the quality of electronics, restau- rants, merchants, etc. The sheer volume of online reviews makes it difficult for a human to process and extract all meaningful information in order to make an educated pur- chase. As a result, there has been a trend toward systems that can automatically summarize opinions from a set of re- views and display them in an easy to process manner (1, 9). In this paper, we present a system that summarizes the sen- timent of reviews for a local service such as a restaurant or hotel. In particular we focus on aspect-based summarization models (8), where a summary is built by extracting relevant aspects of a service, such as service or value, aggregating the sentiment per aspect, and selecting aspect-relevant text. We describe the details of both the aspect extraction and sentiment detection modules of our system. A novel aspect of these models is that they exploit user provided labels and domain specific characteristics of service reviews to increase quality.

Confidence-weighted linear classification

Abstract: We introduce confidence-weighted linear classifiers, which add parameter confidence information to linear classifiers. Online learners in this setting update both classifier parameters and the estimate of their confidence. The particular online algorithms we study here maintain a Gaussian distribution over parameter vectors and update the mean and covariance of the distribution with each instance. Empirical evaluation on a range of NLP tasks show that our algorithm improves over other state of the art online and batch methods, learns faster in the online setting, and lends itself to better classifier combination after parallel training.

Retrieval models for question and answer archives

Abstract: Retrieval in a question and answer archive involves finding good answers for a user's question. In contrast to typical document retrieval, a retrieval model for this task can exploit question similarity as well as ranking the associated answers. In this paper, we propose a retrieval model that combines a translation-based language model for the question part with a query likelihood approach for the answer part. The proposed model incorporates word-to-word translation probabilities learned through exploiting different sources of information. Experiments show that the proposed translation based language model for the question part outperforms baseline methods significantly. By combining with the query likelihood language model for the answer part, substantial additional effectiveness improvements are obtained.

Relative-Error $CUR$ Matrix Decompositions

Abstract: Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the input data. In this paper, we propose and study matrix approximations that are explicitly expressed in terms of a small number of columns and/or rows of the data matrix, and thereby more amenable to interpretation in terms of the original data. Our main algorithmic results are two randomized algorithms which take as input an $m\times n$ matrix $A$ and a rank parameter $k$. In our first algorithm, $C$ is chosen, and we let $A'=CC^+A$, where $C^+$ is the Moore-Penrose generalized inverse of $C$. In our second algorithm $C$, $U$, $R$ are chosen, and we let $A'=CUR$. ($C$ and $R$ are matrices that consist of actual columns and rows, respectively, of $A$, and $U$ is a generalized inverse of their intersection.) For each algorithm, we show that with probability at least $1-\delta$, $\|A-A'\|_F\leq(1+\epsilon)\,\|A-A_k\|_F$, where $A_k$ is the “best” rank-$k$ approximation provided by truncating the SVD of $A$, and where $\|X\|_F$ is the Frobenius norm of the matrix $X$. The number of columns of $C$ and rows of $R$ is a low-degree polynomial in $k$, $1/\epsilon$, and $\log(1/\delta)$. Both the Numerical Linear Algebra community and the Theoretical Computer Science community have studied variants of these matrix decompositions over the last ten years. However, our two algorithms are the first polynomial time algorithms for such low-rank matrix approximations that come with relative-error guarantees; previously, in some cases, it was not even known whether such matrix decompositions exist. Both of our algorithms are simple and they take time of the order needed to approximately compute the top $k$ singular vectors of $A$. The technical crux of our analysis is a novel, intuitive sampling method we introduce in this paper called “subspace sampling.” In subspace sampling, the sampling probabilities depend on the Euclidean norms of the rows of the top singular vectors. This allows us to obtain provable relative-error guarantees by deconvoluting “subspace” information and “size-of-$A$” information in the input matrix. This technique is likely to be useful for other matrix approximation and data analysis problems.

Penalized logistic regression for detecting gene interactions

Abstract: We propose using a variant of logistic regression (LR) with (L)_(2)-regularization to fit gene-gene and gene-environment interaction models. Studies have shown that many common diseases are influenced by interaction of certain genes. LR models with quadratic penalization not only correctly characterizes the influential genes along with their interaction structures but also yields additional benefits in handling high-dimensional, discrete factors with a binary response. We illustrate the advantages of using an (L)_(2)-regularization scheme and compare its performance with that of "multifactor dimensionality reduction" and "FlexTree," 2 recent tools for identifying gene-gene interactions. Through simulated and real data sets, we demonstrate that our method outperforms other methods in the identification of the interaction structures as well as prediction accuracy. In addition, we validate the significance of the factors selected through bootstrap analyses.

Lattice-based Minimum Error Rate Training for Statistical Machine Translation

Abstract: Minimum Error Rate Training (MERT) is an effective means to estimate the feature function weights of a linear model such that an automated evaluation criterion for measuring system performance can directly be optimized in training. To accomplish this, the training procedure determines for each feature function its exact error surface on a given set of candidate translations. The feature function weights are then adjusted by traversing the error surface combined over all sentences and picking those values for which the resulting error count reaches a minimum. Typically, candidates in MERT are represented as N-best lists which contain the N most probable translation hypotheses produced by a decoder. In this paper, we present a novel algorithm that allows for efficiently constructing and representing the exact error surface of all translations that are encoded in a phrase lattice. Compared to N-best MERT, the number of candidate translations thus taken into account increases by several orders of magnitudes. The proposed method is used to train the feature function weights of a phrase-based statistical machine translation system. Experiments conducted on the NIST 2008 translation tasks show significant runtime improvements and moderate BLEU score gains over N-best MERT.

Google's Deep Web crawl

Abstract: The Deep Web, i.e., content hidden behind HTML forms, has long been acknowledged as a significant gap in search engine coverage. Since it represents a large portion of the structured data on the Web, accessing Deep-Web content has been a long-standing challenge for the database community. This paper describes a system for surfacing Deep-Web content, i.e., pre-computing submissions for each HTML form and adding the resulting HTML pages into a search engine index. The results of our surfacing have been incorporated into the Google search engine and today drive more than a thousand queries per second to Deep-Web content.Surfacing the Deep Web poses several challenges. First, our goal is to index the content behind many millions of HTML forms that span many languages and hundreds of domains. This necessitates an approach that is completely automatic, highly scalable, and very efficient. Second, a large number of forms have text inputs and require valid inputs values to be submitted. We present an algorithm for selecting input values for text search inputs that accept keywords and an algorithm for identifying inputs which accept only values of a specific type. Third, HTML forms often have more than one input and hence a naive strategy of enumerating the entire Cartesian product of all possible inputs can result in a very large number of URLs being generated. We present an algorithm that efficiently navigates the search space of possible input combinations to identify only those that generate URLs suitable for inclusion into our web search index. We present an extensive experimental evaluation validating the effectiveness of our algorithms.

A Discriminative Kernel-Based Approach to Rank Images from Text Queries

Abstract: This paper introduces a discriminative model for the retrieval of images from text queries. Our approach formalizes the retrieval task as a ranking problem, and introduces a learning procedure optimizing a criterion related to the ranking performance. The proposed model hence addresses the retrieval problem directly and does not rely on an intermediate image annotation task, which contrasts with previous research. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. The experiments performed over stock photography data show the advantage of our discriminative ranking approach over state-of-the-art alternatives (e.g. our model yields 26.3% average precision over the Corel dataset, which should be compared to 22.0%, for the best alternative model evaluated). Further analysis of the results shows that our model is especially advantageous over difficult queries such as queries with few relevant pictures or multiple-word queries.

Linear Time Maximally Stable Extremal Regions

Abstract: In this paper we present a new algorithm for computing Maximally Stable Extremal Regions (MSER), as invented by Matas et al. The standard algorithm makes use of a union-find data structure and takes quasi-linear time in the number of pixels. The new algorithm provides exactly identical results in true worst-case linear time. Moreover, the new algorithm uses significantly less memory and has better cache-locality, resulting in faster execution. Our CPU implementation performs twice as fast as a state-of-the-art FPGA implementation based on the standard algorithm. The new algorithm is based on a different computational ordering of the pixels, which is suggested by another immersion analogy than the one corresponding to the standard connected-component algorithm. With the new computational ordering, the pixels considered or visited at any point during computation consist of a single connected component of pixels in the image, resembling a flood-fill that adapts to the grey-level landscape. The computation only needs a priority queue of candidate pixels (the boundary of the single connected component), a single bit image masking visited pixels, and information for as many components as there are grey-levels in the image. This is substantially more compact in practice than the standard algorithm, where a large number of connected components must be considered in parallel. The new algorithm can also generate the component tree of the image in true linear time. The result shows that MSER detection is not tied to the union-find data structure, which may open more possibilities for parallelization.

Online budgeted matching in random input models with applications to Adwords

Abstract: We study an online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints. We analyze the performance of the Greedy algorithm (which assigns each query to the highest bidder) in a randomized input model with queries arriving in a random permutation. Our main result is a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1/e for maximizing the value of the assignment. We also consider the more standard i.i.d. model of input, and show that our analysis holds there as well. This is to be contrasted with the worst case analysis of [MSVV05] which shows that Greedy has a ratio of 1/2, and that the optimal algorithm presented there has a ratio of 1 - 1/e. The analysis of Greedy is important in the Adwords setting because it is the natural allocation algorithm for an auction-style process. From a theoretical perspective, our result simplifies and generalizes the classic algorithm of Karp, Vazirani and Vazirani for online bipartite matching. Our results include a new proof to show that the Ranking alforithm of [KVV90] has a ratio of 1 - 1/e in the worst case. It has been recently discovered [KV07] (independent of our results) that one of the crucial lemmas in [KVV90], related to a certain reduction, is incorrect. Our proof is direct, in that it does not go via such a reduction, which also enables us to generalize the analysis to our online assignment problem.