AUTHOR=Sporring Jon , Darkner Sune 

TITLE=An algebra for local histograms

JOURNAL=Frontiers in Computer Science

VOLUME=4

YEAR=2022

URL=https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2022.939563

DOI=10.3389/fcomp.2022.939563

ISSN=2624-9898

ABSTRACT=<p>In this article, we consider local overlapping histograms of functions between discrete domains and codomains. We develop a simple algebra for local histograms. Based on a separation of overlapping domains into non-overlapping domains, we (1) show how these can be used to enumerate the size of the set of possible histograms given the local histogram domains, and (2) enumerate the number of functions, which share a specific choice of a set of local histograms. Finally, we present a decoding algorithm, which given a set of overlapping histograms, and calculate the set of functions, which share these histograms.</p>