Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths

This paper presents improved algorithms for the following problem: given an unweighted directed graph G(V,E) and a sequence of on-line shortest-path/reachability queries interspersed with edge-deletions, develop a data-structure that can answer each query in optimal time, and can be updated efficiently after each edge-deletion.The central idea underlying our algorithms is a scheme for implicitly storing all-pairs reachability/shortest-path information, and an efficient way to maintain this information.Our algorithms are randomized and have one-sided inverse polynomial error for query.