## Theory of Combinatorial Algorithms

We show that any linear program (LP) in $n$ nonnegative variables and $m$ equality constraints defines in a natural way a \emph{unique sink orientation} of the $n$-dimensional cube. From the sink of the cube, we can either read off an optimal solution to the LP, or we obtain certificates for infeasibility or unboundedness. This reduction complements the implicit local neighborhoods induced by the vertex-edge structure of the feasible region with an explicit neighborhood structure that allows random access to all $2^n$ candidate solutions. Using the currently best sink-finding algorithm for general unique sink orientations, we obtain the fastest deterministic LP algorithm in the RAM model, for the central case $n=2m$.