163 research outputs found
External inverse pattern matching
We consider {\sl external inverse pattern matching} problem. Given a text \t of length over an ordered alphabet , such that , and a number . The entire problem is to find a pattern \pe\in \Sigma^m which is not a subword of \t and which maximizes the sum of Hamming distances between \pe and all subwords of \t of length . We present optimal -time algorithm for the external inverse pattern matching problem which substantially improves the only known polynomial -time algorithm introduced by Amir, Apostolico and Lewenstein. Moreover we discuss a fast parallel implementation of our algorithm on the CREW PRAM model
On Compact Routing for the Internet
While there exist compact routing schemes designed for grids, trees, and
Internet-like topologies that offer routing tables of sizes that scale
logarithmically with the network size, we demonstrate in this paper that in
view of recent results in compact routing research, such logarithmic scaling on
Internet-like topologies is fundamentally impossible in the presence of
topology dynamics or topology-independent (flat) addressing. We use analytic
arguments to show that the number of routing control messages per topology
change cannot scale better than linearly on Internet-like topologies. We also
employ simulations to confirm that logarithmic routing table size scaling gets
broken by topology-independent addressing, a cornerstone of popular
locator-identifier split proposals aiming at improving routing scaling in the
presence of network topology dynamics or host mobility. These pessimistic
findings lead us to the conclusion that a fundamental re-examination of
assumptions behind routing models and abstractions is needed in order to find a
routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802
Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams
Estimating frequency moments and distances are well studied problems in the adversarial data stream model and tight space bounds are known for these two problems. There has been growing interest in revisiting these problems in the framework of random-order streams. The best space lower bound known for computing the frequency moment in random-order streams is by Andoni et al., and it is conjectured that the real lower bound shall be . In this paper, we resolve this conjecture. In our approach, we revisit the direct sum theorem developed by Bar-Yossef et al. in a random-partition private messages model and provide a tight space lower bound for any -pass algorithm that approximates the frequency moment in random-order stream model to a constant factor. Finally, we also introduce the notion of space-entropy tradeoffs in random order streams, as a means of studying intermediate models between adversarial and fully random order streams. We show an almost tight space-entropy tradeoff for distance and a non-trivial tradeoff for distances
Spectrophotometric Procedure for Fast Reactor Advanced Coolant Manufacture Control
The paper describes a spectrophotometric procedure for fast reactor advanced coolant manufacture control. The molar absorption coefficient of dimethyllead dibromide with dithizone was defined as equal to 68864 ± 795 lmole{-1}cm{-1}, limit of detection as equal to 0.583 10{-6} g/ml. The spectrophotometric procedure application range was found to be equal to 37.88-196.3 g. of dimethyllead dibromide in the sample. The procedure was used within the framework of the development of the method of synthesis of the advanced coolant for fast reactors
Sublinear time algorithms for earth mover's distance
We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions
when given access only to samples of the distributions. We give closeness testers and additive-error
estimators over domains in [0, 1][superscript d], with sample complexities independent of domain size – permitting
the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on
other parameters, such as the diameter of the domain space, which may be significantly smaller. We also
prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally,
we consider whether natural classes of distributions exist for which there are algorithms with better
dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly,
we consider a variant of the EMD, defined over tree metrics instead of the usual l 1 metric, and give tight
upper and lower bounds
Space-optimal Heavy Hitters with Strong Error Bounds
The problem of finding heavy hitters and approximating the frequencies of items is at the heart of many problems in data stream analysis. It has been observed that several proposed solutions to this problem can outperform their worst-case guarantees on real data. This leads to the question of whether some stronger bounds can be guaranteed. We answer this in the positive by showing that a class of "counter-based algorithms" (including the popular and very space-efficient FREQUENT and SPACESAVING algorithms) provide much stronger approximation guarantees than previously known. Specifically, we show that errors in the approximation of individual elements do not depend on the frequencies of the most frequent elements, but only on the frequency of the remaining "tail." This shows that counter-based methods are the most space-efficient (in fact, space-optimal) algorithms having this strong error bound.
This tail guarantee allows these algorithms to solve the "sparse recovery" problem. Here, the goal is to recover a faithful representation of the vector of frequencies, f. We prove that using space O(k), the algorithms construct an approximation f* to the frequency vector f so that the L1 error ||f -- f*||[subscript 1] is close to the best possible error min[subscript f2] ||f2 -- f||[subscript 1], where f2 ranges over all vectors with at most k non-zero entries. This improves the previously best known space bound of about O(k log n) for streams without element deletions (where n is the size of the domain from which stream elements are drawn). Other consequences of the tail guarantees are results for skewed (Zipfian) data, and guarantees for accuracy of merging multiple summarized streams.David & Lucile Packard Foundation (Fellowship)Center for Massive Data Algorithmics (MADALGO)National Science Foundation (U.S.). (Grant number CCF-0728645
Tight Lower Bound for Linear Sketches of Moments
The problem of estimating frequency moments of a data stream has attracted a
lot of attention since the onset of streaming algorithms [AMS99]. While the
space complexity for approximately computing the moment, for
has been settled [KNW10], for the exact complexity remains
open. For the current best algorithm uses words of
space [AKO11,BO10], whereas the lower bound is of [BJKS04].
In this paper, we show a tight lower bound of words
for the class of algorithms based on linear sketches, which store only a sketch
of input vector and some (possibly randomized) matrix . We note
that all known algorithms for this problem are linear sketches.Comment: In Proceedings of the 40th International Colloquium on Automata,
Languages and Programming (ICALP), Riga, Latvia, July 201
Robust 3D face capture using example-based photometric stereo
We show that using example-based photometric stereo, it is possible to achieve realistic reconstructions of the human face. The method can handle non-Lambertian reflectance and attached shadows after a simple calibration step. We use spherical harmonics to model and de-noise the illumination functions from images of a reference object with known shape, and a fast grid technique to invert those functions and recover the surface normal for each point of the target object. The depth coordinate is obtained by weighted multi-scale integration of these normals, using an integration weight mask obtained automatically from the images themselves. We have applied these techniques to improve the PHOTOFACE system of Hansen et al. (2010). © 2013 Elsevier B.V. All rights reserved
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