Maintaining minimum spanning trees in dynamic graphs
We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o(√n) per operation. To be precise, the algorithm uses O(n1/3 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(n1/3 log n) per update, with O(1) worst case time per query.
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