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SODA
2008
ACM

On distance to monotonicity and longest increasing subsequence of a data stream

8 years 3 months ago
On distance to monotonicity and longest increasing subsequence of a data stream
In this paper we consider problems related to the sortedness of a data stream. First we investigate the problem of estimating the distance to monotonicity; given a sequence of length n, we give a deterministic (2 + )-approximation algorithm for estimating its distance to monotonicity in space O( 1 2 log2 ( n)). This improves over the randomized (4 + )-approximation algorithm of [3]. We then consider the problem of approximating the length of the longest increasing subsequence of an input stream of length n. We use techniques from multi-party communication complexity combined with a fooling set approach to prove that any O(1)pass deterministic streaming algorithm that approximates the length of the longest increasing subsequence within 1+ requires ( n) space. This proves the conjecture in [3] and matches the current upper bound.
Funda Ergün, Hossein Jowhari
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Funda Ergün, Hossein Jowhari
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