Algorithms for fair allocation and fair division in graphs

Abstract

This project extends the study of fair allocation and division in graph structures by building upon the concept of (1,β)-compact allocations for paths, as introduced in the seminal work on compact graph allocations. Specifically, we extend the results for (1,β) compact allocation from paths to two-dimensional grid-like graphs and further generalize it to graphs of maximum degree d employing a Depth First Search based approach under the fairness notion of proportionality. The results demonstrate the scalability of the proposed approach across multiple dimensions, contributing to our broader understanding of fair division in complex graph topologies.