arXiv subjects

Eli Upfal

Publications and source records attributed to Eli Upfal.

45 records · Page 3Linked to original sources

arXiv2011

Space-Round Tradeoffs for MapReduce Computations

This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by allowing for a flexible use of parallelism. Indeed, the model diverges from a traditional processor-centric view by featuring parameters which embody only global and local memory constraints, thus favoring a more data-centric view. Second, we apply the model to the fundamental computation task of matrix multiplication presenting upper and lower bounds for both dense and sparse matrix multiplication, which highlight interesting tradeoffs between space and round complexity. Finally, building on the matrix multiplication results, we derive further space-round tradeoffs on matrix inversion and matching.

cs.DS↗

arXiv2011

The VC-Dimension of Queries and Selectivity Estimation Through Sampling

We develop a novel method, based on the statistical concept of the Vapnik-Chervonenkis dimension, to evaluate the selectivity (output cardinality) of SQL queries - a crucial step in optimizing the execution of large scale database and data-mining operations. The major theoretical contribution of this work, which is of independent interest, is an explicit bound to the VC-dimension of a range space defined by all possible outcomes of a collection (class) of queries. We prove that the VC-dimension is a function of the maximum number of Boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection, but it is neither a function of the number of queries in the collection nor of the size (number of tuples) of the database. We leverage on this result and develop a method that, given a class of queries, builds a concise random sample of a database, such that with high probability the execution of any query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database. The error probability holds simultaneously for the selectivity estimates of all queries in the collection, thus the same sample can be used to evaluate the selectivity of multiple queries, and the sample needs to be refreshed only following major changes in the database. The sample representation computed by our method is typically sufficiently small to be stored in main memory. We present extensive experimental results, validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in PostgreSQL and the Microsoft SQL Server.

cs.DB↗

arXiv2011

Tight Bounds on Information Dissemination in Sparse Mobile Networks

Motivated by the growing interest in mobile systems, we study the dynamics of information dissemination between agents moving independently on a plane. Formally, we consider $k$ mobile agents performing independent random walks on an $n$-node grid. At time $0$, each agent is located at a random node of the grid and one agent has a rumor. The spread of the rumor is governed by a dynamic communication graph process ${G_t(r) | t \geq 0}$, where two agents are connected by an edge in $G_t(r)$ iff their distance at time $t$ is within their transmission radius $r$. Modeling the physical reality that the speed of radio transmission is much faster than the motion of the agents, we assume that the rumor can travel throughout a connected component of $G_t$ before the graph is altered by the motion. We study the broadcast time $T_B$ of the system, which is the time it takes for all agents to know the rumor. We focus on the sparse case (below the percolation point $r_c \approx \sqrt{n/k}$) where, with high probability, no connected component in $G_t$ has more than a logarithmic number of agents and the broadcast time is dominated by the time it takes for many independent random walks to meet each other. Quite surprisingly, we show that for a system below the percolation point the broadcast time does not depend on the relation between the mobility speed and the transmission radius. In fact, we prove that $T_B = \tilde{O}(n / \sqrt{k})$ for any $0 \leq r < r_c$, even when the transmission range is significantly larger than the mobility range in one step, giving a tight characterization up to logarithmic factors. Our result complements a recent result of Peres et al. (SODA 2011) who showed that above the percolation point the broadcast time is polylogarithmic in $k$.

cs.DM↗

arXiv2011

Infectious Random Walks

We study the dynamics of information (or virus) dissemination by $m$ mobile agents performing independent random walks on an $n$-node grid. We formulate our results in terms of two scenarios: broadcasting and gossiping. In the broadcasting scenario, the mobile agents are initially placed uniformly at random among the grid nodes. At time 0, one agent is informed of a rumor and starts a random walk. When an informed agent meets an uninformed agent, the latter becomes informed and starts a new random walk. We study the broadcasting time of the system, that is, the time it takes for all agents to know the rumor. In the gossiping scenario, each agent is given a distinct rumor at time 0 and all agents start random walks. When two agents meet, they share all rumors they are aware of. We study the gossiping time of the system, that is, the time it takes for all agents to know all rumors. We prove that both the broadcasting and the gossiping times are $\tildeΘ(n/\sqrt{m})$ w.h.p., thus achieving a tight characterization up to logarithmic factors. Previous results for the grid provided bounds which were weaker and only concerned average times. In the context of virus infection, a corollary of our results is that static and dynamically moving agents are infected at about the same speed.

cs.DM↗

arXiv2010

Mining Top-K Frequent Itemsets Through Progressive Sampling

We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes) all very frequent (resp., very infrequent) itemsets, together with an estimate of these itemsets' frequencies with a bounded error. Our first result is an upper bound on the sample size which guarantees that the top-K frequent itemsets mined from a random sample of that size approximate the actual top-K frequent itemsets, with probability larger than a specified value. We show that the upper bound is asymptotically tight when w is constant. Our main algorithmic contribution is a progressive sampling approach, combined with suitable stopping conditions, which on appropriate inputs is able to extract approximate top-K frequent itemsets from samples whose sizes are smaller than the general upper bound. In order to test the stopping conditions, this approach maintains the frequency of all itemsets encountered, which is practical only for small w. However, we show how this problem can be mitigated by using a variation of Bloom filters. A number of experiments conducted on both synthetic and real bench- mark datasets show that using samples substantially smaller than the original dataset (i.e., of size defined by the upper bound or reached through the progressive sampling approach) enable to approximate the actual top-K frequent itemsets with accuracy much higher than what analytically proved.

cs.DS↗

arXiv2010

MADMX: A Novel Strategy for Maximal Dense Motif Extraction

We develop, analyze and experiment with a new tool, called MADMX, which extracts frequent motifs, possibly including don't care characters, from biological sequences. We introduce density, a simple and flexible measure for bounding the number of don't cares in a motif, defined as the ratio of solid (i.e., different from don't care) characters to the total length of the motif. By extracting only maximal dense motifs, MADMX reduces the output size and improves performance, while enhancing the quality of the discoveries. The efficiency of our approach relies on a newly defined combining operation, dubbed fusion, which allows for the construction of maximal dense motifs in a bottom-up fashion, while avoiding the generation of nonmaximal ones. We provide experimental evidence of the efficiency and the quality of the motifs returned by MADMX

cs.DS↗

arXiv2010

An Efficient Rigorous Approach for Identifying Statistically Significant Frequent Itemsets

As advances in technology allow for the collection, storage, and analysis of vast amounts of data, the task of screening and assessing the significance of discovered patterns is becoming a major challenge in data mining applications. In this work, we address significance in the context of frequent itemset mining. Specifically, we develop a novel methodology to identify a meaningful support threshold s* for a dataset, such that the number of itemsets with support at least s* represents a substantial deviation from what would be expected in a random dataset with the same number of transactions and the same individual item frequencies. These itemsets can then be flagged as statistically significant with a small false discovery rate. We present extensive experimental results to substantiate the effectiveness of our methodology.

cs.DB↗

arXiv2008

Multi-Armed Bandits in Metric Spaces

In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions. In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the "Lipschitz MAB problem". We present a complete solution for the multi-armed problem in this setting. That is, for every metric space (L,X) we define an isometry invariant which bounds from below the performance of Lipschitz MAB algorithms for X, and we present an algorithm which comes arbitrarily close to meeting this bound. Furthermore, our technique gives even better results for benign payoff functions.

cs.DS↗

arXiv2002

Steady state analysis of balanced-allocation routing

We compare the long-term, steady-state performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks, to the performance of a path-selection algorithm based on the "balanced-allocation" principle; we refer to this new algorithm as the Balanced Dynamic Alternative Routing (BDAR) algorithm. While DAR checks alternative routes sequentially until available bandwidth is found, the BDAR algorithm compares and chooses the best among a small number of alternatives. We show that, at the expense of a minor increase in routing overhead, the BDAR algorithm gives a substantial improvement in network performance, in terms both of network congestion and of bandwidth requirement.

math.PR↗