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Journal of the ACM (JACM)
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ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We consider the following problem: given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O (n ) space and needs O (n logk + k logn ) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a lower bound for k = O (n ). Since, in contrast to previous approaches, the algorithm decomposes the range of element values rather than the array, it has natural generalizations to higher-dimensional problems --- it reduces a range median query to a logarithmic number of range counting queries.