Longest increasing subsequences in windows based on canonical antichain partition

  • Authors:

  • Erdong Chen;Hao Yuan;Linji Yang

  • Affiliations:

  • Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China

  • Venue:
  • ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
  • Year:
  • 2005

Quantified Score

Hi-index 0.01

Visualization

Abstract

We consider the Lisw problem, which is to find the longest increasing subsequences (LIS) in a sliding window of fixed-size w over a sequence π1π2...πn. Formally, it is to find a LIS for every window in a set SFIX ={π〈i+1, i+w〉|0≤i≤n−w}∪{π〈1, i〉, π〈n−i, n〉|iw}, where a window π〈l,r〉 is a subsequence πlπl+1...πr. By maintaining a canonical antichain partition in windows, we present an optimal output-sensitive algorithm to solve this problem in O(output) time, where output is the sum of the length of the n+w–1 longest increasing subsequences in those windows of SFIX. In addition, we propose a more generalized problem called Lisset, which is to find the LIS for every window in a set SVAR containing variable-size windows. By applying our algorithm, we provide an efficient solution for Lisset problem which is better than the straight forward generalization of classical LIS algorithms. An upper bound of our algorithm on Lisset is discussed.