Efficient Compilation of Algorithms into Compact Linear Programs

While data-driven approaches continue to find new applications across many domains, traditional mathematical optimization frameworks remain highly effective for solving realworld problems with well-defined constraints. Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Although Algebraic Modeling Languages (AMLs) offer a higher level of abstraction for describing LPs, users must still manually specify each set of constraints. A recent work introduced an LP compiler that not only enables conversion of algorithms expressed in a more intuitive high-level programming language into LPs, but also guarantees polynomial-size LPs for P problems having exponential extension complexity. However, the LPs are extremely large in practice, posing challenges for existing LP solvers due to memory limitations, long solution and presolve times, numerical instability, and rounding errors. With the longterm goal of enabling systematic generation of Compact Integer Programming (CIP) formulations for exponential-size Integer Programs (IPs) having polynomial-time separation oracles, we propose a hierarchical linear pipelining technique, called Hierarchical Synchronization Barriers (HSB). HSB decomposes code into tree-like synchronized regions with statically known execution transitions, functions of compile-time parameters. This control-flow abstraction localizes LP constraints and variables to their relevant regions, significantly reducing LP size. We examine the effectiveness of HSB on the makespan problem, which has exponential extension complexity, and the weighted minimum spanning tree problem, both of which have exponentialsize natural LP formulations. Our results show up to a 25-fold reduction in LP size and substantial improvements in solver performance across both commercial and non-commercial LP solvers.