An Optimal Offline Algorithm for List Update

For the static list update problem, given an ordered list ρ0 (an ordering of the list L = { aa, a2, ..., al }), and a sequence σ = (σ1, σ2, ..., σm) of requests for items in L, we characterize the list reorganizations in an optimal offline solution in terms of an initial permutation of the list followed by a sequence of m element transfers, where an element transfer is a type of list reorganization where only the requested item can be moved. Then we make use of this characterization to design an O(l2(l − 1)!m) time optimal offline algorithm.