insight - Algorithms Data Structures

### Efficient Similarity Sketching for Fast Approximate Similarity Search

The authors present a new similarity sketching algorithm that achieves fast expected running time of O(|A| + t log t) while providing strong concentration guarantees for similarity estimation, outperforming previous approaches.

### Maintaining a Correlation Clustering Algorithm with Improved Approximation Ratio in the Fully Dynamic Setting

The authors present a new algorithm, ModifiedPivot, that breaks the 3-approximation barrier for correlation clustering in the fully dynamic setting by locally improving the output of the Pivot algorithm.

### Efficient O(1) Query Algorithm for Finding Level Ancestors in Rooted Trees

This paper presents a simple O(1) query time algorithm for finding the k-th ancestor of a node in a rooted tree, with O(n log n) preprocessing time.

### Efficient Algorithms for Fair and Diverse Subset Selection from High-Dimensional Data

The authors develop the first constant approximation algorithm for the Fair Max-Min Diversification (FairDiv) problem that runs in near-linear time using only linear space. Their approach employs a novel combination of the Multiplicative Weight Update method and advanced geometric data structures to implicitly and approximately solve a linear program.

### A Fast Skip-based Algorithm for Weighted Reservoir Random Sampling with Replacement

This paper presents a novel skip-based algorithm for efficient weighted reservoir sampling with replacement, which improves upon the standard algorithm by reducing the computational cost.