@MISC{Henzinger97fullydynamic, author = {Monika Rauch Henzinger and et al.}, title = {Fully dynamic algorithms for bounded genus graphs}, year = {1997} }

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Abstract

We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O(log n = log log n) worst-case time per query, where n is the number of vertices in the graph. This is the first fully dynamic deterministic algorithm for connectivity in nonplanar graphs that runs in polylogarithmic time per operation. A consequence of our connectivity algorithm is fully dynamic algorithms for several other problems in bounded genus graphs.