How far will you walk to find your shortcut: Space Efficient Synopsis Construction Algorithms

TL;DR

This paper introduces a near-optimal, space-efficient algorithm for wavelet synopsis construction that surpasses previous methods, with extensions to histogram construction and broader dynamic programming applications.

Contribution

It presents the first near-optimal, space-efficient algorithm for wavelet synopsis construction without coefficient subset restrictions, improving previous algorithms significantly.

Findings

Almost linear space complexity achieved

Enhanced algorithms for histogram and range query histograms

Improved space-time tradeoffs for dynamic programming applications

Abstract

In this paper we consider the wavelet synopsis construction problem without the restriction that we only choose a subset of coefficients of the original data. We provide the first near optimal algorithm. We arrive at the above algorithm by considering space efficient algorithms for the restricted version of the problem. In this context we improve previous algorithms by almost a linear factor and reduce the required space to almost linear. Our techniques also extend to histogram construction, and improve the space-running time tradeoffs for V-Opt and range query histograms. We believe the idea applies to a broad range of dynamic programs and demonstrate it by showing improvements in a knapsack-like setting seen in construction of Extended Wavelets.