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A Simple Algorithm for Minimum Cuts in Near-Linear Time
TLDR
We give a self-contained version of Karger's algorithm with the new procedure, which is easy to state and relatively simple to implement. Expand
Optimal Offline Dynamic 2, 3-Edge/Vertex Connectivity
TLDR
We give offline algorithms for processing a sequence of 2- and 3-edge and vertex connectivity queries in a fully-dynamic undirected graph. Expand
Offline Dynamic Higher Connectivity
TLDR
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
Improved Time and Space Bounds for Dynamic Range Mode
TLDR
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
Space-Efficient Data Structures for Lattices
TLDR
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). Expand
On Approximate Range Mode and Range Selection
TLDR
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
Faster Dynamic Range Mode
TLDR
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
Lazy Search Trees
TLDR
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
On Euclidean Methods for Cubic and Quartic Jacobi Symbols
TLDR
We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. Expand
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