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In this short expository note, we describe a unified algorithmic perspectiveon several classical problems which have traditionally been studied indifferent communities. This perspective views the main characters -- theproblems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and MatrixBalancing -- through the same lens of optimization problems over jointprobability distributions P(x,y) with constrained marginals. While this is howOptimal Transport is typically introduced, this lens is markedly lessconventional for the other three problems. This perspective leads to a simpleand unified framework spanning problem formulation, algorithm development, andruntime analysis.

Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions