Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components

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 <i>O</i>(<i>mn</i>) 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 <i>O</i>(<i>n</i>^1.5) for planar graphs, <i>O</i>(<i>n</i> log <i>n</i>) for graphs with bounded treewidth and <i>O</i>(<i>mn</i>) for general digraphs.