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- W2015901059 abstract "In the combinatorial version of the generalized birthday problem, w1's and n−w 0's are randomly arranged in either a line or a cycle; km is defined to be the largest number of 1's appearing within any m consecutive positions. In the binomial version, each point is independently 1 with probability p and 0 with probability 1−p. Current algorithms for computing Pr(km < k) in the cases of practical interest where k and m are small, but n and w are large, require time exponential in both n and w. We present a new algorithm which requires O(log n) time to solve the binomial version and O(n log n) time to solve the combinatorial version simultaneously for all values of w. The generalized birthday problem corresponds to a test for non-random clustering and has applications in statistical trials. Applications to reliability theory are also discussed." @default.
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- W2015901059 date "1997-02-01" @default.
- W2015901059 modified "2023-09-27" @default.
- W2015901059 title "An O(n log n) algorithm for the generalized birthday problem" @default.
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- W2015901059 doi "https://doi.org/10.1016/s0167-9473(96)00051-5" @default.
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