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We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(mα(m,n)) time, where α is the inverse-Ackermann function. This improves upon a long standing bound of O(mα(m,n)) established by Tarjan. Our algorithms are based on an efficient split-findmin data structure, which maintains a collection of sequences of weighted elements that may be split into smaller subsequences. As far as we are aware, our split-findmin algorithm isarXiv:1407.1910v1 fatcat:6lvaiyot2fgljhpzu7lwgxpzx4