Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components

Authors:
Jakub Łącki
Affiliations:
University of Warsaw
Venue:
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Year:
2013

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Abstract

This article presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries in constant time. Previously, such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly connected components are shown, whose time complexity is O(n1.5) for planar graphs, O(n log n) for graphs with bounded treewidth and O(mn) for general digraphs.