We give the first $O(t\log{t})$ time algorithm for processing a given sequence of $t$ edge updates and 3-vertex/edge connectivity queries in an undirected unweighted graph.Expand

We develop a Monte Carlo data structure that supports queries in $\tilde{O}(n^{2/3})$ deterministic time, updates in $\O(n)$ space, and occupies $O( n) space for the range mode and range least frequent queries.Expand

For any $\epsilon \in (0,1)$, a $(1+\epsilone)$-approximate range mode query asks for the position of an element whose frequency in the query range is at most a factor $(1+) smaller than the true mode.Expand

In the dynamic range mode problem, we are given a sequence $a$ of length bounded by $N$ and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence of $a$.Expand

The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and maximum while providing dynamic operations insert, delete, change-key, split, and merge.Expand