Reconstruction of multiple strings of constant weight from prefix-suffix compositions

TL;DR

This paper addresses the problem of uniquely reconstructing multiple binary strings of equal length and weight from their prefix and suffix compositions, providing theoretical conditions and algorithms for reconstruction.

Contribution

It introduces necessary and sufficient conditions for unique reconstruction and proposes two algorithms for reconstructing constant-weight strings from prefix-suffix compositions.

Findings

Conditions for unique reconstruction up to reversal

Algorithms for reconstructing constant-weight strings

Theoretical framework for data retrieval in polymer-based storage

Abstract

Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and suffixes of every possible length. We provide necessary and sufficient conditions for which unique reconstruction up to reversal of the strings is possible. Additionally, we present two algorithms for reconstructing strings from the compositions of prefixes and suffixes of constant-length constant-weight strings.