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Can You Solve Closest String Faster than Exhaustive Search?
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest Hamming ball around $x^*$ that encloses all the strings in $X$.
On Complexity of 1-Center in Various Metrics
Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of $n$ strings each of length $n$, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.
Impossibility Results for Grammar-Compressed Linear Algebra
In this paper we consider lossless compression schemes, and ask if we can run our computations on the compressed data as efficiently as if the original data was that small.
Subquadratic High-Dimensional Hierarchical Clustering
We consider the widely-used average-linkage, single-linkage, and Ward's methods for computing hierarchical clusterings of high-dimensional Euclidean inputs.
