Partially dynamic maintenance of minimum weight hyperpaths

We address the problem of dynamically maintaining minimum weight hyperpaths in a directed hypergraph in a decremental setting. For such a problem, we provide a new efficient algorithm that works for a wide class of hyperpath weight measures. This algorithm explicitly updates minimum weight hyperpaths in O(L ·C+max{n,C} · size(H)) worst case time under a sequence of L hyperarc weight increments and hyperarc deletions, where C is the maximum weight of minimum hyperpaths in H and size(H) is the size of the representation of the hypergraph. Hyperpath weight measures are only required to belong to the class of strict weakly superior functions.  2004 Elsevier B.V. All rights reserved.