Indexes for Jumbled Pattern Matching in Strings, Trees and Graphs

TL;DR

This paper develops indexing methods for jumbled pattern matching in strings, trees, and graphs, enabling efficient exact and approximate match retrieval with different space complexities.

Contribution

It introduces quadratic and linear space indexing techniques for jumbled pattern matching in trees, balancing accuracy and resource usage.

Findings

Quadratic-space index enables match retrieval proportional to match size.

Linear-space index allows approximate matching with reduced memory.

Efficient algorithms for jumbled pattern matching in complex data structures.

Abstract

We consider how to index strings, trees and graphs for jumbled pattern matching when we are asked to return a match if one exists. For example, we show how, given a tree containing two colours, we can build a quadratic-space index with which we can find a match in time proportional to the size of the match. We also show how we need only linear space if we are content with approximate matches.