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We study computing all-pairs shortest paths (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits (1+o(1))-approximation Õ(n)-time algorithms [2], [3], which are matched with \tilde Ω(n)-time lower bounds [4], [5],\footnote{\tilde \Theta, Õ...
We present a Las Vegas algorithm for dynamically maintaining a minimum spanning forest of an n-node graph undergoing edge insertions and deletions. Our algorithm guarantees an O(n^{o(1)})} worst-case} update time with high probability. This significantly improves the two recent Las Vegas algorithms by Wulff-Nilsen \cite{Wulff-Nilsen16a} with update time O(n^{0.5-≥ilon}) for some constant...
The dynamic optimality conjecture is perhaps the most fundamental open question about binary search trees (BST). It postulates the existence of an asymptotically optimal online BST, i.e. One that is constant factor competitive with any BST on any input access sequence. The two main candidates for dynamic optimality in the literature are splay trees [Sleator and Tarjan, 1985], and Greedy [Lucas, 1988,...
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