This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that are often crucial for data analytics in practice. Such adaptation conversely enables the compression algorithm to drain every bit of information a sorted superset could bring for rapid convergence. Multidimensional extension follows a novel decomposition of the problem and is friendly to multithreading. Data structures supporting the algorithms have trivial space complexity. The framework offers exact algorithms for the multidimensional knapsack problem and the generalized assignment problem.