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

Authors:
Surender Baswana;Ramesh Hariharan;Sandeep Sen
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India;Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India;Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India
Venue:
Journal of Algorithms
Year:
2007

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Abstract

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.