Quasi-Fully Dynamic Algorithms for Two-Connectivity, Cycle Equivalence and Related Problems

In thispaper we introduce a new class of dynamicgraphalgorithmscalledquasi-fully dynamic algorithms,which are much more general than the backtracking algorithmsand are much simpler than the fully dynamic algorithms. These algorithms are especially suitable for applications in which a certain core connected portion of the graph remains xed, and fully dynamic updates occur on the remaining edges in the graph. We present very simple quasi-fully dynamic algorithms with O(logn) worst case time, per operation, for 2-edge connectivity and cycle equivalence. The former is deterministic while the latter is Monte-Carlo type randomized. For 2-vertex connectivity, we give a randomized Las Vegas algorithm with O(log4 n) expected amortized time per operation. We introduce the concept of quasi-k-edge-connectivity, which is a slightly relaxed version of k-edge connectivity, and show that it can be maintained in O(logn) worst case time per operation. We also analyze the performance of a natural extens...

• Type: Conference
• Year: 1997
• Where: ESA
• Authors: Madhukar R. Korupolu, Vijaya Ramachandran
• Keywords: Algorithms, Dynamic Algorithm, ESA 1997, Quasi-fully Dynamic Algorithm, Worst Case Time