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25
Logarithmic lower bounds in the cellprobe model
 SIAM Journal on Computing
"... Abstract. We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This enables us to prove Ω(lg n) bounds, breaking a longstanding barrier of Ω(lg n/lg lg n). We can also prove the first Ω(lgB n) lower bound in the external memory model, without assumptions on the ..."
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Abstract. We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This enables us to prove Ω(lg n) bounds, breaking a longstanding barrier of Ω(lg n/lg lg n). We can also prove the first Ω(lgB n) lower bound in the external memory model, without assumptions on the data structure. We use our technique to prove better bounds for the partialsums problem, dynamic connectivity and (by reductions) other dynamic graph problems. Our proofs are surprisingly simple and clean. The bounds we obtain are often optimal, and lead to a nearly complete understanding of the problems. We also present new matching upper bounds for the partialsums problem. Key words. cellprobe complexity, lower bounds, data structures, dynamic graph problems, partialsums problem AMS subject classification. 68Q17
Lower bounds for dynamic connectivity
 STOC
, 2004
"... We prove an Ω(lg n) cellprobe lower bound on maintaining connectivity in dynamic graphs, as well as a more general tradeoff between updates and queries. Our bound holds even if the graph is formed by disjoint paths, and thus also applies to trees and plane graphs. The bound is known to be tight fo ..."
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Cited by 24 (1 self)
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We prove an Ω(lg n) cellprobe lower bound on maintaining connectivity in dynamic graphs, as well as a more general tradeoff between updates and queries. Our bound holds even if the graph is formed by disjoint paths, and thus also applies to trees and plane graphs. The bound is known to be tight for these restricted cases, proving optimality of these data structures (e.g., Sleator and Tarjan’s dynamic trees). Our tradeoff is known to be tight for trees, and the best two data structures for dynamic connectivity in general graphs are points on our tradeoff curve. In this sense these two data structures are optimal, and this tightness serves as strong evidence that our lower bounds are the best possible. From a more theoretical perspective, our result is the first logarithmic cellprobe lower bound for any problem in the natural class of dynamic language membership problems, breaking the long standing record of Ω(lg n / lg lg n). In this sense, our result is the first datastructure lower bound that is “truly ” logarithmic, i.e., logarithmic in the problem size counted in bits. Obtaining such a bound is listed as one of three major challenges for future research by Miltersen [13] (the other two challenges remain unsolved). Our techniques form a general framework for proving cellprobe lower bounds on dynamic data structures. We show how our framework also applies to the partialsums problem to obtain a nearly complete understanding of the problem in cellprobe and algebraic models, solving several previously posed open problems.
A Hierarchical Volumetric Shadow Algorithm for Single Scattering
"... eye light rays integration samples blocker integration sample blocked sample view ray i view ray i+1 epipolar rectification view rays (incremental evluation) light rays (integration direction) integration Figure 1: Rendering volumetric shadows in participating media requires integrating scattering o ..."
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Cited by 17 (1 self)
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eye light rays integration samples blocker integration sample blocked sample view ray i view ray i+1 epipolar rectification view rays (incremental evluation) light rays (integration direction) integration Figure 1: Rendering volumetric shadows in participating media requires integrating scattering over view rays. Left: The visibility component of this integral has a special structure: once a light ray hits an occluder, that light ray does not contribute to the integral along any view ray past the occluder. Middle: Our method exploits this structure by computing the integrals in an epipolar coordinate system, in which light rays (dashed grey) and view rays (solid black) are orthogonal and the integration can be performed asymptotically efficiently using a partial sum tree. Right: This enables us to compute highquality scattering integrals much faster than the previous state of the art. Volumetric effects such as beams of light through participating media are an important component in the appearance of the natural world. Many such effects can be faithfully modeled by a single scattering medium. In the presence of shadows, rendering these effects can be prohibitively expensive: current algorithms are based on ray marching, i.e., integrating the illumination scattered towards the camera along each view ray, modulated by visibility to the light source at each sample. Visibility must be determined for each sample using shadow rays or shadowmap lookups. We observe that in a suitably chosen coordinate system, the visibility function has a regular structure that we can exploit for significant acceleration compared to brute force sampling. We propose an efficient algorithm based on partial sum trees for computing the scattering integrals in a singlescattering homogeneous medium. On a CPU, we achieve speedups of 17–120x over ray marching.
Comparative Analysis of Arithmetic Coding Computational Complexity
, 2004
"... Some longheld assumptions about the most demanding computations for arithmetic coding are now obsolete due to new hardware. For instance, it is not advantageous to replace multiplicationwhich now can be done with high precision in a single CPU clock cyclewith comparisons and tablebased ap ..."
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Cited by 16 (1 self)
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Some longheld assumptions about the most demanding computations for arithmetic coding are now obsolete due to new hardware. For instance, it is not advantageous to replace multiplicationwhich now can be done with high precision in a single CPU clock cyclewith comparisons and tablebased approximations. A good understanding of the cost of the arithmetic coding computations is needed to design e#cient implementations for the current and future processors. In this work we profile these computations by comparing the running times of many implementations, trying to change at most one part at a time, and avoiding small e#ects being masked by much larger ones. For instance, we test arithmetic operations ranging from 16bit integers to 48bit floating point; and renormalization outputs from single bit to 16 bits. To evaluate the complexity of adaptive coding we compare static models and di#erent adaptation strategies. We observe that significant speed gains are possible if we do not insist on updating the code immediately after each coded symbol. The results show that the fastest techniques are those that e#ectively use the CPU's hardware: fullprecision arithmetic, byte output, table lookup decoding, and periodic updating.
LOGARITHMIC LOWER BOUNDS IN THE CELLPROBE MODEL
"... We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This technique enables us to prove an amortized randomized Ω(lg n) lower bound per operation for several data structural problems on n elements, including partial sums, dynamic connectivity among disjoint pat ..."
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Cited by 5 (0 self)
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We develop a new technique for proving cellprobe lower bounds on dynamic data structures. This technique enables us to prove an amortized randomized Ω(lg n) lower bound per operation for several data structural problems on n elements, including partial sums, dynamic connectivity among disjoint paths (or a forest or a graph), and several other dynamic graph problems (by simple reductions). Such a lower bound breaks a longstanding barrier of Ω(lg n / lg lg n) for any dynamic language membership problem. It also establishes the optimality of several existing data structures, such as Sleator and Tarjan’s dynamic trees. We also prove the first Ω(log B n) lower bound in the externalmemory model without assumptions on the data structure (such as the comparison model). Our lower bounds also give a queryupdate tradeoff curve matched, e.g., by several data structures for dynamic connectivity in graphs. We also prove matching upper and lower bounds for partial sums when parameterized by the word size and the maximum additive change in an update.
Lossy Compression of Turbulence Data
, 1998
"... A number of Grand Challenge applications are capable of generating such large quantities of data that data output may a#ect the applications performance. An example of such an application is modeling of turbulent convection. One means of dealing with this situation is data compression. This thesis e ..."
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Cited by 2 (0 self)
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A number of Grand Challenge applications are capable of generating such large quantities of data that data output may a#ect the applications performance. An example of such an application is modeling of turbulent convection. One means of dealing with this situation is data compression. This thesis examines applying wavelet based lossy compression techniques to turbulent convection data. It also seeks to design compression algorithms that are optimized for compressing turbulent convection data.
A light differential download algorithm for software defined radio devices
 in IEEE Consumer Communications and Networking Conference
, 2005
"... Abstract — Radio configuration (RCFG) files for software defined radio (SDR) devices can be downloaded over the air, allowing these devices to support multimode functionality using a single transceiver. The drawback of this is that the wireless link is constrained and downloading the entire RCFG ..."
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Abstract — Radio configuration (RCFG) files for software defined radio (SDR) devices can be downloaded over the air, allowing these devices to support multimode functionality using a single transceiver. The drawback of this is that the wireless link is constrained and downloading the entire RCFG could take some time. In an effort to achieve efficiency, this paper presents a new algorithm for differential download, referred to as light differential download algorithm (LDDA). The LDDA is the first differential download algorithm specifically designed for SDR devices. It presents several new features that make not only RCFG differential download a possibility, but also allows the update of any software by differential download. Experiments using Java 2 Micro Edition are performed to demonstrate the feasibility and superior performance of the LDDA when compared with other approaches.
A Scalable Asynchronous Distributed Algorithm for Topic Modeling
"... Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons. First, one needs to deal with a large number of topics (typically on the order of thousands). Second, one needs a scalable and efficien ..."
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Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons. First, one needs to deal with a large number of topics (typically on the order of thousands). Second, one needs a scalable and efficient way of distributing the computation across multiple machines. In this paper, we present a novel algorithm F+Nomad LDA which simultaneously tackles both these problems. In order to handle large number of topics we use an appropriately modified Fenwick tree. This data structure allows us to sample from a multinomial distribution over T items in O(log T) time. Moreover, when topic counts change the data structure can be updated in O(log T) time. In order to distribute the computation across multiple processors, we present a novel asynchronous framework inspired by the Nomad algorithm of [25]. We show that F+Nomad LDA significantly outperforms recent stateoftheart topic modeling approaches on massive problems which involve millions of documents, billions of words, and thousands of topics.
On the Tradeoff between Stability and Fit
"... In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a onetime instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and must decide how to respond to a new set of constraints, giv ..."
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In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a onetime instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of PPS (probability proportional to size) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to topk, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions, and discuss efficient incremental algorithms that can find new solutions as the input changes. 1