21,081 research outputs found

    A Time-Space Tradeoff for Triangulations of Points in the Plane

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    In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm

    Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

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    We consider space-bounded computations on a random-access machine (RAM) where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is NN elements, the length of the output is limited by the computation, and the capacity of the workspace is O(S)O(S) bits for some predetermined parameter SS. We present a state-of-the-art priority queue---called an adjustable navigation pile---for this restricted RAM model. Under some reasonable assumptions, our priority queue supports minimum\mathit{minimum} and insert\mathit{insert} in O(1)O(1) worst-case time and extract\mathit{extract} in O(N/S+lgS)O(N/S + \lg{} S) worst-case time for any SlgNS \geq \lg{} N. We show how to use this data structure to sort NN elements and to compute the convex hull of NN points in the two-dimensional Euclidean space in O(N2/S+NlgS)O(N^2/S + N \lg{} S) worst-case time for any SlgNS \geq \lg{} N. Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.Comment: 21 page

    Selection from read-only memory with limited workspace

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    Given an unordered array of NN elements drawn from a totally ordered set and an integer kk in the range from 11 to NN, in the classic selection problem the task is to find the kk-th smallest element in the array. We study the complexity of this problem in the space-restricted random-access model: The input array is stored on read-only memory, and the algorithm has access to a limited amount of workspace. We prove that the linear-time prune-and-search algorithm---presented in most textbooks on algorithms---can be modified to use Θ(N)\Theta(N) bits instead of Θ(N)\Theta(N) words of extra space. Prior to our work, the best known algorithm by Frederickson could perform the task with Θ(N)\Theta(N) bits of extra space in O(NlgN)O(N \lg^{*} N) time. Our result separates the space-restricted random-access model and the multi-pass streaming model, since we can surpass the Ω(NlgN)\Omega(N \lg^{*} N) lower bound known for the latter model. We also generalize our algorithm for the case when the size of the workspace is Θ(S)\Theta(S) bits, where lg3NSN\lg^3{N} \leq S \leq N. The running time of our generalized algorithm is O(Nlg(N/S)+N(lgN)/lgS)O(N \lg^{*}(N/S) + N (\lg N) / \lg{} S), slightly improving over the O(Nlg(N(lgN)/S)+N(lgN)/lgS)O(N \lg^{*}(N (\lg N)/S) + N (\lg N) / \lg{} S) bound of Frederickson's algorithm. To obtain the improvements mentioned above, we developed a new data structure, called the wavelet stack, that we use for repeated pruning. We expect the wavelet stack to be a useful tool in other applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201

    Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees

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    In the limited-workspace model, we assume that the input of size nn lies in a random access read-only memory. The output has to be reported sequentially, and it cannot be accessed or modified. In addition, there is a read-write workspace of O(s)O(s) words, where s{1,,n}s \in \{1, \dots, n\} is a given parameter. In a time-space trade-off, we are interested in how the running time of an algorithm improves as ss varies from 11 to nn. We present a time-space trade-off for computing the Euclidean minimum spanning tree (EMST) of a set VV of nn sites in the plane. We present an algorithm that computes EMST(V)(V) using O(n3logs/s2)O(n^3\log s /s^2) time and O(s)O(s) words of workspace. Our algorithm uses the fact that EMST(V)(V) is a subgraph of the bounded-degree relative neighborhood graph of VV, and applies Kruskal's MST algorithm on it. To achieve this with limited workspace, we introduce a compact representation of planar graphs, called an ss-net which allows us to manipulate its component structure during the execution of the algorithm

    Knowledge discovery for friction stir welding via data driven approaches: Part 2 – multiobjective modelling using fuzzy rule based systems

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    In this final part of this extensive study, a new systematic data-driven fuzzy modelling approach has been developed, taking into account both the modelling accuracy and its interpretability (transparency) as attributes. For the first time, a data-driven modelling framework has been proposed designed and implemented in order to model the intricate FSW behaviours relating to AA5083 aluminium alloy, consisting of the grain size, mechanical properties, as well as internal process properties. As a result, ‘Pareto-optimal’ predictive models have been successfully elicited which, through validations on real data for the aluminium alloy AA5083, have been shown to be accurate, transparent and generic despite the conservative number of data points used for model training and testing. Compared with analytically based methods, the proposed data-driven modelling approach provides a more effective way to construct prediction models for FSW when there is an apparent lack of fundamental process knowledge

    Document Retrieval on Repetitive Collections

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    Document retrieval aims at finding the most important documents where a pattern appears in a collection of strings. Traditional pattern-matching techniques yield brute-force document retrieval solutions, which has motivated the research on tailored indexes that offer near-optimal performance. However, an experimental study establishing which alternatives are actually better than brute force, and which perform best depending on the collection characteristics, has not been carried out. In this paper we address this shortcoming by exploring the relationship between the nature of the underlying collection and the performance of current methods. Via extensive experiments we show that established solutions are often beaten in practice by brute-force alternatives. We also design new methods that offer superior time/space trade-offs, particularly on repetitive collections.Comment: Accepted to ESA 2014. Implementation and experiments at http://www.cs.helsinki.fi/group/suds/rlcsa
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