  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.
