We propose a family of constant-degree routing networks of logarithmic diameter, with the additional property that the addition or removal of a node to the network requires no global coordination, only a constant number of linkage changes in expectation, and a logarithmic number with high probability. Our randomized construction improves upon existing solutions, such as balanced search trees, by ensuring that the congestion of the network is always within a logarithmic factor of the optimum with high probability. Our construction derives from recent advances in the study of peer-to-peer lookup networks, where rapid changes require e#cient and distributed maintenance, and where the lookup e#ciency is impacted both by the lengths of paths to requested data and the presence or elimination of bottlenecks in the network.

Abstract. We present a polynomial-time randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fully-polynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small specified relative error of the true value of the permanent. Categories and Subject Descriptors: F.2.2 [Analysis of algorithms and problem complexity]: Nonnumerical

In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chosen element of the given ensemble will achieve an arbitrarily small target probability of error with a probability that approaches one exponentially fast in the length of the code. (By concatenating with an appropriate outer code one can achieve a probability of error that approaches zero exponentially fast in the length of the code with arbitrarily small loss in rate.) Conversely, transmitting at rates above this capacity the probability of error is bounded away from zero by a strictly positive constant which is independent of the length of the code and of the number of iterations performed. Our results are based on the observation that the concentration of the performance of the decoder around its average performance, as observed by Luby et al. [1] in the case of a binary-symmetric channel and a binary message-passing algorithm, is a general phenomenon. For the particularly important case of belief-propagation decoders, we provide an effective algorithm to determine the corresponding capacity to any desired degree of accuracy. The ideas presented in this paper are broadly applicable and extensions of the general method to low-density parity-check codes over larger alphabets, turbo codes, and other concatenated coding schemes are outlined.

between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination.

Abstract. We introduce a new sublinear space data structure—the Count-Min Sketch — for summarizing data streams. Our sketch allows fundamental queries in data stream summarization such as point, range, and inner product queries to be approximately answered very quickly; in addition, it can be applied to solve several important problems in data streams such as finding quantiles, frequent items, etc. The time and space bounds we show for using the CM sketch to solve these problems significantly improve those previously known — typically from 1/ε 2 to 1/ε in factor. 1

We present a study of operating system errors found by automatic, static, compiler analysis applied to the Linux and OpenBSD kernels. Our approach differs from previ-ous studies that consider errors found by manual inspec-tion of logs, testing, and surveys because static analysis is applied uniformly to the entire kernel source, though our approach necessarily considers a less comprehensive variety of errors than previous studies. In addition, au-tomation allows us to track errors over multiple versions of the kernel source to estimate how long errors remain in the system before they are fixed. We found that device drivers have error rates up to three to seven times higher than the rest of the ker-nel. We found that the largest quartile of functions have error rates two to six times higher than the small-est quartile. We found that the newest quartile of files have error rates up to twice that of the oldest quartile, which provides evidence that code "hardens " over time. Finally, we found that bugs remain in the Linux kernel an average of 1.8 years before being fixed. 1

This paper presents the design of Mercury, a scalable protocol for supporting multi-attribute rangebased searches. Mercury differs from previous range-based query systems in that it supports multiple attributes as well as performs explicit load balancing. Efficient routing and load balancing are implemented using novel light-weight sampling mechanisms for uniformly sampling random nodes in a highly dynamic overlay network. Our evaluation shows that Mercury is able to achieve its goals of logarithmic-hop routing and near-uniform load balancing. We also show that a publish-subscribe system based on the Mercury protocol can be used to construct a distributed object repository providing efficient and scalable object lookups and updates. By providing applications a range-based query language to express their subscriptions to object updates, Mercury considerably simplifies distributed state management. Our experience with the design and implementation of a simple distributed multiplayer game built on top of this object management framework shows that indicates that this indeed is a useful building block for distributed applications. Keywords: Range queries, Peer-to-peer systems, Distributed applications, Multiplayer games 1

Mayur Datar Aristides Gionis y Piotr Indyk z Rajeev Motwani x Abstract We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's in the last N elements seen from the stream. We show that using O( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl log 2 N) memory bits for any deterministic or randomized algorithms. We extend our scheme to maintain the sum of the last N positive integers. We provide matching upper and lower bounds for this more general problem as well. We apply our techniques to obtain efficient algorithms for the Lp norms (for p 2 [1; 2]) of vectors under the sliding window model. Using the algorithm for the basic counting problem, one can adapt many other techniques to work for the sliding window model, with a multiplicative overhead of O( 1 ffl log N) in memory and a 1 + ffl factor loss in accuracy. These include maintaining approximate histograms, hash tables, and statistics or aggregates such as sum and averages.

This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight non-approximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems.

We introduce the notion of expansiveness to characterize a family of robot configuration spaces whose connectivity can be effectively captured by a roadmap of randomly-sampled milestones. The analysis of expansive configuration spaces has inspired us to develop a new randomized planning algorithm. This algorithm tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space. Thus, it is well-suited for problems where a single query is submitted for a given environment. The algorithm has been implemented and successfully applied to complex assembly maintainability problems from the automotive industry.