A class of "simple" online algorithms for the k-server problem is identified. This class, for which the term trackless is introduced, includes many known server algorithms. The k-server conjecture fails for ...
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A class of "simple" online algorithms for the k-server problem is identified. This class, for which the term trackless is introduced, includes many known server algorithms. The k-server conjecture fails for trackless algorithms. A lower bound of 23/11 on the competitiveness of any deterministic trackless 2-server algorithm and a lower bound of 1 + root 2/2 on the competitiveness of any randomized trackless 2-server problem are given. (C) 2000 Published by Elsevier Science B.V. An rights reserved.
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want the segments to be as monotonic as possible and to alternate signs. We...
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Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want the segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l norm, and we present an optimal linear time algorithm based on a novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labelling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modelling.
Pattern matching is important in text processing, molecular biology, operating systems and web search engines. Many algorithms have been developed to search for a specific pattern in a text, but the need for an effici...
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Pattern matching is important in text processing, molecular biology, operating systems and web search engines. Many algorithms have been developed to search for a specific pattern in a text, but the need for an efficient algorithm is an outstanding issue. In this paper, we present a simple and practical string matching algorithm. The proposed algorithm is a hybrid that combines our modification of Horspool's algorithm with two observations on string matching. The algorithm scans the text from left to right and matches the pattern from right to left. Experimental results on natural language texts, genomes and human proteins demonstrate that the new algorithm is competitive with practical algorithms.
Given nodes s and t, the quickest path problem is to find a path p from s to t, such that the total transmission time in the communication network for sigma units of data, with sigma greater than or equal to zero, fro...
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Given nodes s and t, the quickest path problem is to find a path p from s to t, such that the total transmission time in the communication network for sigma units of data, with sigma greater than or equal to zero, from s to t is minimum among all possible paths from s to t in the network. An algorithm was developed for the single pair quickest path problem with a certain time complexity as a function of sigma. An extension of this algorithm solves the single source i.e. one to all quickest path problem. The all-pairs quickest path problem for a particular sigma can be solved with a certain time complexity by applying the single source quickest path algorithm several times. The all-pairs quickest path problem is discussed as a function of sigma. The network is preprocessed in such a way that given any pair of nodes, the quickest path is found to transmit data between the nodes for sigma greater than or equal to zero. The time complexity and data structure are discussed.
Modular exponentiation is a frequent task, in particular for many cryptographic applications. To accelerate modular exponentiation for very large integers one may use repeated squaring. which is based on representing ...
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Modular exponentiation is a frequent task, in particular for many cryptographic applications. To accelerate modular exponentiation for very large integers one may use repeated squaring. which is based on representing the exponent in the standard binary numeration system. We show here that for certain applications, replacing the standard system by one based on Fibonacci numbers may yield a new line of time/space tradeoffs. (C) 2007 Elsevier B.V. All rights reserved.
For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a ...
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For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a polynomial time algorithm for computing the symmetry number. (C) 2001 Elsevier Science B.V. All rights reserved.
We present a new sorting algorithm, called Splitsort, which adapts to existing order within the input sequence. The algorithm is optimal with respect to several known measures of presortedness, including the number of...
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We present a new sorting algorithm, called Splitsort, which adapts to existing order within the input sequence. The algorithm is optimal with respect to several known measures of presortedness, including the number of inversions, for which no such simple and space efficient algorithm was known before. The amount of extra space needed is only n pointers. Splitsort uses a simple data structure and is easy to code. In the worst case Splitsort performs 2.5nlog2n comparisons, but if the input is presorted according to some of the measures it completes the sorting task considerably faster. We also show how a variant of the algorithm can be implemented to run in-place.
We present a THETA(n2) worst-case-time algorithm to determine the minimum finishing time for a preemptive schedule of n independent jobs on a hypercube of fixed dimension.
We present a THETA(n2) worst-case-time algorithm to determine the minimum finishing time for a preemptive schedule of n independent jobs on a hypercube of fixed dimension.
We consider the problem MAX CSP over multi-valued domains with variables ranging over sets of size s(i) less than or equal to s and constraints involving k(j) less than or equal to k variables. We study two algorithms...
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We consider the problem MAX CSP over multi-valued domains with variables ranging over sets of size s(i) less than or equal to s and constraints involving k(j) less than or equal to k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A, B). The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp. on Theoret. Aspects of Comput. Sci., 1998, pp. 488-498] and gives ratio A which is bounded below by s(1-k). For k = 2, our bound in terms of the individual set sizes is the minimum over all constraints involving two variables of (1/2roots(1) + 1/2roots(2))(2), where s(1) and s(2) are the set sizes for the two variables. We then give a simple combinatorial algorithm which has approximation ratio B, with B > A/e. The bound is greater than s(1-k)/e in general, and greater than s(1-k)(1-(s-1)/2(k- 1)) for s < k-1, thus close to the s(1-k) linear programming bound for large k. For k = 2, the bound is 4/9 if s = 2, 1/2(s-1) if s greater than or equal to 3, and in general greater than the minimum of 1/4s(1) + 1/4s(2) over constraints with set sizes s(1) and s(2), thus within a factor of two of the linear programming bound. For the case of k = 2 and s = 2 we prove an integrality gap of 4/9(1 + O(n(-1/2))). This shows that our analysis is tight for any method that uses the linear programming upper bound. (C) 2002 Elsevier Science B.V. All rights reserved.
The Mean-Shift (MS) algorithm and its variants have wide applications in pattern recognition and computer vision tasks such as clustering, segmentation, and tracking. In this paper, we study the dynamics of the algori...
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The Mean-Shift (MS) algorithm and its variants have wide applications in pattern recognition and computer vision tasks such as clustering, segmentation, and tracking. In this paper, we study the dynamics of the algorithm with Gaussian kernels, based on a Generalized MS (GMS) model that includes the standard MS as a special case. First, we prove that the GMS has solutions in the convex hull of the given data points. By the principle of contraction mapping, a sufficient condition, dependent on a parameter introduced into Gaussian kernels, is provided to guarantee the uniqueness of the solution. It is shown that the solution is also globally stable and exponentially convergent under the condition. When the condition does not hold, the GMS algorithm can possibly have multiple equilibriums, which can be used for clustering as each equilibrium has its own attractive basin. Based on this, the condition can be used to estimate an appropriate parameter which ensures the GMS algorithm to have its equilibriums suitable for clustering. Examples are given to illustrate the correctness of the condition. It is also shown that the use of the multiple-equilibrium property for clustering, on the data sets such as IRIS, leads to a lower error rate than the standard MS approach, and the K-Means and Fuzzy C-Means algorithms. (c) 2012 Elsevier B.V. All rights reserved.
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