Queueing and glueing for optimal partitioning (functional pearl)

Abstract

The queueing-glueing algorithm is the nickname we give to an algorithmic pattern that provides amortised linear time solutions to a number of optimal list partition problems that have a peculiar property: at various moments we know that two of three candidate solutions could be optimal. The algorithm works by keeping a queue of lists, glueing them from one end, while chopping from the other end, hence the name. We give a formal derivation of the algorithm, and demonstrate it with several non-trivial examples.