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  • 1.
    Bengtsson, Fredrik
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Algorithms for aggregate information extraction from sequences2007Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we propose efficient algorithms for aggregate information extraction from sequences and multidimensional arrays. The algorithms proposed are applicable in several important areas, including large databases and DNA sequence segmentation. We first study the problem of efficiently computing, for a given range, the range-sum in a multidimensional array as well as computing the k maximum values, called the top-k values. We design two efficient data structures for these problems. For the range-sum problem, our structure supports fast update while preserving low complexity of range-sum query. The proposed top-k structure provides fast query computation in linear time proportional to the sum of the sizes of a two-dimensional query region. We also study the k maximum sum subsequences problem and develop several efficient algorithms. In this problem, the k subsegments of consecutive elements with largest sum are to be found. The segments can potentially overlap, which allows for a large number of possible candidate segments. Moreover, we design an optimal algorithm for ranking the k maximum sum subsequences. Our solution does not require the value of k to be known a priori. Furthermore, an optimal linear-time algorithm is developed for the maximum cover problem of finding k subsequences of consecutive elements of maximum total element sum.

  • 2.
    Bengtsson, Fredrik
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Efficient aggregate queries on data cubes2004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    As computers are developing rapidly and become more available to the modern information society, the possibility and ability to handle large data sets in database applications increases. The demand for efficient algorithmic solutions to process huge amounts of information increases as the data sets become larger. In this thesis, we study the efficient implementation of aggregate operations on the data cube, a modern and flexible model for data warehouses. In particular, the problem of computing the k largest sum subsequences of a given sequence is investigated. An efficient algorithm for the problem is developed. Our algorithm is optimal for large values of the user-specified parameter k. Moreover, a fast in-place algorithm with good trade-off between update- and query-time, for the multidimensional orthogonal range sum problem, is presented. The problem studied is to compute the sum of the data over an orthogonal range in a multidimensional data cube. Furthermore, a fast algorithmic solution to the problem of maintaining a data structure for computing the k largest values in a requested orthogonal range of the data cube is also proposed.

  • 3.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    A note on ranking k maximum sums2005Report (Other academic)
    Abstract [en]

    In this paper, we design a fast algorithm for ranking the k maximum sum subsequences. Given a sequence of real numbers and an integer parameter k, the problem is to compute k subsequences of consecutive elements with the sums of their elements being the largest, second largest, ..., and the k:th largest among all possible range sums. For any value of k, 1 <= k <= n(n+1)/2, our algorithm takes O(n + k log n) time in the worst case to rank all such subsequences. Our algorithm is optimal for k <= n.

  • 4.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Computing maximum-scoring segments in almost linear time2006Report (Other academic)
    Abstract [en]

    Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires n log n time in the worst case. For a given sequence of length n, we present an almost linear-time algorithm for this problem. Our algorithm uses a disjoint-set data structure and requires O(n a(n, n) ) time in the worst case, where a(n,n) is the inverse Ackermann function.

  • 5.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Computing maximum-scoring segments in almost linear time2006In: Computing and Combinatorics: 12th annual international conference, COCOON 2006, Taipei, Taiwan, August 15 - 18, 2006 ; proceedings / [ed] Danny Z. Chen, Encyclopedia of Global Archaeology/Springer Verlag, 2006, p. 255-264Conference paper (Refereed)
    Abstract [en]

    Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires Θ(n log n) time in the worst case. For a given sequence of length n, we present an almost linear-time algorithm for this problem. Our algorithm uses a disjoint-set data structure and requires O(nα(n, n)) time in the worst case, where α(n, n) is the inverse Ackermann function.

  • 6.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Computing maximum-scoring segments optimally2007Report (Other academic)
    Abstract [en]

    Given a sequence of length n, the problem studied in this report is to find a set of k disjoint subsequences of consecutive elements such that the total sum of all elements in the set is maximized. This problem arises in the analysis of DNA sequences. The previous best known algorithm requires time proportional to n times the inverse Ackermann function of (n,n), in the worst case. We present a linear-time algorithm, which is optimal, for this problem.

  • 7.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Computing the k maximum subarrays fast2004Report (Other academic)
    Abstract [en]

    We study the problem of computing the k maximum sum subarrays. Given an array of real numbers and an integer, k, the problem involves finding the k largest values of the sum from i to j of the array, for any i and j. The problem for fixed k=1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. In this paper, we develop an algorithm requiring time proportional to n times square root of k for an array of length n. Moreover, for two-dimensional version of the problem, which computes the k largest sums over all rectangular subregions of an m times n array of real numbers, we show that it can be solved efficiently in the worst case as well.

  • 8.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Efficient algorithms for k maximum sums2004In: Algorithms and Computation: 15th International Symposium, ISAAC 2004 / [ed] Rudolf Fleischer; Gerhard Trippen, Berlin: Encyclopedia of Global Archaeology/Springer Verlag, 2004, p. 137-148Conference paper (Refereed)
    Abstract [en]

    We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers (x1,x2,⋯,xn) and an integer parameter k, l ≤ k ≤ 1/2n(n -1), the problem involves finding the k largest values of Σl=ij xl for 1 ≤ i ≤ j ≤ n. The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. Recently, Bae and Takaoka presented a θ(nk)-time algorithm for the k maximum sum subsequences problem. In this paper, we design efficient algorithms that solve the above problem in O (min{k + n log2 n, n √k}) time in the worst case. Our algorithm is optimal for k ≥ n log2 n and improves over the previously best known result for any value of the user-defined parameter k. Moreover, our results are also extended to the multi-dimensional versions of the k maximum sum subsequences problem; resulting in fast algorithms as well

  • 9.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Efficient algorithms for k maximum sums2006In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 46, no 1, p. 27-41Article in journal (Refereed)
    Abstract [en]

    We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers {x1,x2,...,xn} and an integer parameter k, 1 ≤ k ≤ 1/2n(n-1),the problem involves finding the k largest values of ∑ℓ=ijxℓ for 1 ≤ i ≤ j ≤ n.The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. Recently, Bae and Takaoka presented a Θ(nk)-time algorithm for the k maximum sum subsequences problem. In this paper we design an efficient algorithm that solves the above problem in O(min {k+nlog2n,n√k} ) time in the worst case. Our algorithm is optimal for k = Ω(n log 2 n) and improves over the previously best known result for any value of the user-defined parameter k < 1. Moreover, our results are also extended to the multi-dimensional versions of the k maximum sum subsequences problem; resulting in fast algorithms as well

  • 10.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Ranking k maximum sums2007In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 377, no 1-3, p. 229-237Article in journal (Refereed)
    Abstract [en]

    Given a sequence of n real numbers and an integer parameter k, the problem studied in this paper is to compute k subsequences of consecutive elements with the sums of their elements being the largest, the second largest, and the kth largest among all possible range sums of the input sequence. For any value of k, 1 <= k <= n (n + 1)/2, we design a fast algorithm that takes O (n + k log n) time in the worst case to compute and rank all such subsequences. We also prove that our algorithm is optimal for k = O (n) by providing a matching lower bound.Moreover, our algorithm is an improvement over the previous results on the maximum sum subsequences problem (where only the subsequences are requested and no ordering with respect to their relative sums will be determined).Furthermore, given the fact that we have computed the fth largest sums, our algorithm retrieves the (l + 1)th largest sum in O (log n) time, after O (n) time of preprocessing.

  • 11.
    Bengtsson, Fredrik
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Chen, Jingsen
    Space-efficient range-sum queries in OLAP2004In: Data Warehousing and Knowledge Discovery. Proceedings: 6th international conference, DaWaK 2004, Zaragoza, Spain, September 1 - 3, 2004 : proceedings / [ed] Yahiko Kambayashi; Mukesh Mohania; Wolfram Wöß, Encyclopedia of Global Archaeology/Springer Verlag, 2004, p. 87-96Conference paper (Refereed)
    Abstract [en]

    In this paper, we present a fast algorithm to answer range-sum queries in OLAP data cubes. Our algorithm supports constant-time queries while maintaining sub-linear time update and using minimum space. Furthermore, we study the trade-off between query time and update time. The complexity for query is O(2ℓd) and for updates O((2ℓ2ℓ√n)d) on a data cube of nd elements, where ℓ is a trade-off parameter. Our algorithm improve over previous best known results

  • 12. Klockar, Tomas
    et al.
    Carr, David A.
    Luleå tekniska universitet.
    Hedman, Anna
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Johansson, Tomas
    Bengtsson, Fredrik
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Usability of mobile phones2003In: Proceedings of the 19th International Symposium on Human Factors in Telecommunications, 2003, p. 197-204Conference paper (Refereed)
1 - 12 of 12
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