We consider processors communicating over a mesh network with the objective of broadcasting information among each other, One instance of the problem involves a number of nodes all with the same message to be broadcas...
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We consider processors communicating over a mesh network with the objective of broadcasting information among each other, One instance of the problem involves a number of nodes all with the same message to be broadcasted. For that problem, a lower-bound on the time to complete the broadcast, and an algorithm which achieves this bound are presented. In another instance, every node in the mesh has packets to be broadcast arriving independently, according to a Poisson random process, The stability region for performing such broadcasts is characterized, and broadcast algorithms which operate efficiently within that region are presented, These algorithms involve interacting queues whose analysis is known to be very difficult, Toward that end we develop an approximation which models an n-dimensional infinite Markov chain as a single-dimensional infinite Markov chain together with an n-dimensional finite Markov chain. This approximate model can be analyzed and the results compare favorably with simulation.
Our experimental analysis of several popular XPath processors reveals a striking fact: Query evaluation in each of the systems requires time exponential in the size of queries in the worst case. We show that XPath can...
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Our experimental analysis of several popular XPath processors reveals a striking fact: Query evaluation in each of the systems requires time exponential in the size of queries in the worst case. We show that XPath can be processed much more efficiently, and propose main-memory algorithms for this problem with polynomial-time combined query evaluation complexity. Moreover, we show how the main ideas of our algorithm can be profitably integrated into existing XPath processors. Finally, we present two fragments of XPath for which linear-time query processing algorithms exist and another fragment with linear-space/quadratic-time query processing.
In this paper we investigate theoretical properties of the Double Traveling Salesman Problem with Multiple Stacks. In particular, we provide polynomial time algorithms for different subproblems when the stack size lim...
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In this paper we investigate theoretical properties of the Double Traveling Salesman Problem with Multiple Stacks. In particular, we provide polynomial time algorithms for different subproblems when the stack size limit is relaxed. Since these algorithms can represent building blocks for more complex methods, we also include them in a simple heuristic which we test experimentally. We finally analyze the impact of handling the stack size limit, and we propose repair procedures. The theoretical investigation highlights interesting structural properties of the problem, and our computational results show that the single components of the heuristic can be successfully incorporated in more complex algorithms or bounding techniques. (C) 2011 Elsevier Ltd. All rights reserved.
With the advances in the next generation sequencing technology, huge amounts of data have been and get generated in biology. A bottleneck in dealing with such datasets lies in developing effective algorithms for extra...
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With the advances in the next generation sequencing technology, huge amounts of data have been and get generated in biology. A bottleneck in dealing with such datasets lies in developing effective algorithms for extracting useful information from them. algorithms for finding patterns in biological data pave the way for extracting crucial information from the voluminous datasets. In this paper, we focus on a fundamental pattern, namely, the closest l-mers. Given a set of m biological strings S-1, S-2,..., Sm and an integer l, the problem of interest is that of finding an l-mer from each string such that the distance among them is the least. For example we want to find m l-mers X-1, X-2 ,..., X-m such that X-i is an l-mer in S-i (for 1 <= i <= m) and the Hamming distance among these m l-mers is the least (from among all such possible l-mers). This problem has many applications. An application of great importance is motif search. algorithms for finding the closest l-mers have been used in solving the (l, d)-motif search problem (see e.g., [1], [2]). In this paper novel exact and approximate algorithms are proposed for this problem for the case of m > 2. In particular, a comprehensive experimental evaluation is performed for m = 3, along with a further empirical study of m = 4 and 5. We also extend our solution to euclidean distance measurement metric if the sequences contain real numbers.
We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type, A ...
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We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type, A vehicle starts at a prespecified point x(0) and follows a unit speed trajectory x(t) inside a region in R(m), until an unspecified time T that the region is exited, A trajectory minimizing a cost function of the form integral(0)(T) r(x(t)) dt+q(x(T)) is sought, The discretized Hamilton-Jacobi equation corresponding to this problem is usually solved using iterative methods, Nevertheless, assuming that the function r is positive, we are able to exploit the problem structure and develop one-pass algorithms for the discretized problem, The first algorithm resembles Dijkstra's shortest path algorithm and runs in time O(n log n), where n is the number of grid points. The second algorithm uses a somewhat different discretization and borrows some ideas from a variation of Dial's shortest path algorithm that we develop here;it runs in time O(n), which is the best possible, under some fairly mild assumptions, Finally, we show that the latter algorithm can be efficiently parallelized: for two-dimensional problems and with p processors, its running time becomes O(n/p), provided that p = O(root n/log n).
The L(2)-discrepancy is a quantitative measure of precision for multivariate quadrature rules. It can be computed explicitly. Previously known algorithms needed O(m(2)) operations, where m is the number of nodes. In t...
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The L(2)-discrepancy is a quantitative measure of precision for multivariate quadrature rules. It can be computed explicitly. Previously known algorithms needed O(m(2)) operations, where m is the number of nodes. In this paper we present algorithms which require O(m(log m)(d)) operations.
This correspondence presents two soft morphological algorithms that process multiple images simultaneously. The first algorithm performs best when the structuring elements contain less than 19 points;whereas, the seco...
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This correspondence presents two soft morphological algorithms that process multiple images simultaneously. The first algorithm performs best when the structuring elements contain less than 19 points;whereas, the second algorithm should be used for larger structuring elements. Theoretical and experimental analyses show these algorithms are faster than the conventional algorithm.
This paper provides efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characte...
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This paper provides efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: The classes of the Boolean hierarchy over level El of the dot-depth hierarchy are decidable in NL (previously only the decidability was known). The same remains true if predicates mod d for fixed d are allowed. If modular predicates for arbitrary d are allowed, then the classes of the Boolean hierarchy over level El are decidable. For the restricted case of a two-letter alphabet, the classes of the Boolean hierarchy over level Sigma(2) of the Straubing-Therien hierarchy are decidable in NL. This is the first decidability result for this hierarchy. The membership problems for all mentioned Boolean-hierarchy classes are logspace many-one hard for NL. The membership problems for quasi-aperiodic languages and for d-quasi-aperiodic languages are logspace many-one complete for PSPACE. (C) 2016 Elsevier E.V. All rights reserved.
Most applications of statistics to science and engineering are based on the assumption that the corresponding random variables are normally distributed, i.e., distributed according to Gaussian law in which the probabi...
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Most applications of statistics to science and engineering are based on the assumption that the corresponding random variables are normally distributed, i.e., distributed according to Gaussian law in which the probability density function rho(x) exponentially decreases with x: rho(x) similar to exp(-k . x(2)). Normal distributions indeed frequently occur in practice. However, there are also many practical situations, including situations from mathematical finance, in which we encounter heavy-tailed distributions, i.e., distributions in which rho(x) decreases as rho(x) similar to x(-alpha). To properly take this uncertainty into account when making decisions, it is necessary to estimate the parameters of such distributions based on the sample data x(1), ... , x(n)-and thus, to predict the size and the probabilities of large deviations. The most well-known statistical estimates for such distributions are the Hill estimator H for alpha and the Weismann estimator W for the corresponding quantiles. These estimators are based on the simplifying assumption that the sample values x(i) are known exactly. In practice, we often know the values x(i) only approximately-e.g., we know the estimates (x) over tilde (i) and we know the upper bounds Delta(i) on the estimation errors. In this case, the only information that we have about the actual (unknown) value x(i) is that x(i) belongs to the interval x(i) = [(x) over tilde (i) - Delta(i), (x) over tilde (i) + Delta(i)]. Different combinations of values x(i) is an element of x(i) lead, in general, to different values of H and W. It is therefore desirable to find the ranges[(H) under bar, (H) over bar] and [(W) under bar, (W) over bar] of possible values of H and W. In this paper, we describe efficient algorithms for computing these ranges.
In this paper, we provide efficient algorithms for approximate C-m(R-n, R-D)-selection. In particular, given a set E, a constant M-0 > 0, and convex sets K(x) subset of R-D for x is an element of E, we show that an...
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In this paper, we provide efficient algorithms for approximate C-m(R-n, R-D)-selection. In particular, given a set E, a constant M-0 > 0, and convex sets K(x) subset of R-D for x is an element of E, we show that an algorithm running in C(tau)N log N steps is able to solve the smooth selection problem of selecting a point y is an element of (1 + tau)lozenge K(x) for x is an element of E for an appropriate dilation of K(x), (1 + tau)lozenge K(x), and guaranteeing that a function interpolating the points (x, y) will be C-m(R-n, R-D) with norm bounded by CM.
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