Ford–Fulkerson suddenly feels relevant when applied to Splitwise’s Simplify Debts feature. The app’s goal is to settle balances with the fewest, cleanest transactions, a problem that maps neatly onto a flow network. By treating money as flow, users can see the algorithm’s practical value.

To model the problem, a virtual source injects all owed money, while a sink absorbs what is due. Every person becomes a node, and edges between debtors and creditors carry unlimited capacity—infinite simply means no artificial restriction. The algorithm then finds augmenting paths that represent valid payments.

Reverse edges allow the algorithm to backtrack and reroute money, mirroring real‑world refunds or cancellations. The solution is optimal only in a system‑level sense: it maximizes the amount that reaches the sink, not fairness to each user. Understanding this clarifies why max‑flow is a natural fit for debt simplification.

After the flow is computed, the source and sink nodes are discarded, leaving only person‑to‑person transfers. Developers can then implement a lightweight post‑processing step to merge duplicate payments or reduce transaction count, though minimizing the number of edges remains an NP‑hard challenge that often requires heuristic tweaks.