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Estimating the Longest Increasing Sequence in Polylogarithmic Time

2017
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SIAM journal on computing (Print)
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Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let n denote the size of the array. Simple O(n log n) algorithms are known for this problem. What can a sublinear time algorithm achieve? We develop a polylogarithmic time randomized algorithm that for any constant δ > 0, estimates the length of the LIS of an array upto an additive error of δn. More precisely, the running time of the algorithm is (log n) c (1/δ) O(1/δ) where the exponent c is

doi:10.1137/130942152
fatcat:udn5bxlqv5ainczf3ma55mlngm