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.
