The debts' clearing problem: a new approach

TL;DR

This paper introduces a new algorithm for the debts' clearing problem, extending it to dynamic graphs and providing a data structure that improves upon previous static solutions.

Contribution

It adapts the debts' clearing problem to dynamic graphs and develops a novel data structure and algorithm that outperform previous static approaches.

Findings

Developed a data structure for dynamic debts' clearing

Created an improved algorithm for static debts' clearing

Extended the problem to dynamic graph scenarios

Abstract

The debts' clearing problem is about clearing all the debts in a group of $n$ entities (e.g. persons, companies) using a minimal number of money transaction operations. In our previous works we studied the problem, gave a dynamic programming solution solving it and proved that it is NP-hard. In this paper we adapt the problem to dynamic graphs and give a data structure to solve it. Based on this data structure we develop a new algorithm, that improves our previous one for the static version of the problem.