Maintaining Minimum Spanning Forests in Dynamic Graphs
Monika Rauch Henzinger, Valerie Jean King · SIAM Journal on Computing · 2001
We present the first fully dynamic algorithm for maintaining a minimum spanning forest in time $o(\sqrt n)$ per operation. To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and bipartiteness in amortized time O(n 1/3 log n) per update, with O(1) worst case time per query.