Related papers: RSK tableaux and the weak order on fully commutati…
Coreset, which is a summary of the original dataset in the form of a small weighted set in the same sample space, provides a promising approach to enable machine learning over distributed data. Although viewed as a proxy of the original…
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
We investigate the dynamics of the well-known RSK bijection on permutations when iterated on various reading words of the recording tableau. In the setting of the ordinary (row) reading word, we show that there is exactly one fixed point…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Given a multiplicative subset $S$ in a commutative ring $R$, we consider $S$-weakly cotorsion and $S$-strongly flat $R$-modules, and show that all $R$-modules have $S$-strongly flat covers if and only if all flat $R$-modules are…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…
Coresets for $k$-means and $k$-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of $k$ centers. Recently coresets have also been constructed for constrained $k$-means and…
Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Sampling-based decoding underlies complex reasoning in large language models (LLMs), where decoding strategies critically shape model behavior. Temperature- and truncation-based methods reshape the next-token distribution through global…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps both for shared-memory and distributed-memory…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…
Through dualities on representations on tensor powers and symmetric powers respectively, the partition algebra and multiset partition algebra have been used to study long-standing questions in the representation theory of the symmetric…
We introduce a new model to study algorithm design under unreliable information, and apply this model for the problem of finding the uncorrupted maximum element of a list containing $n$ elements, among which are $k$ corrupted elements.…
For the ordered set $[n]$ of $n$ elements, we consider the class $\Bscr_n$ of bases $B$ of tropical Pl\"ucker functions on $2^{[n]}$ such that $B$ can be obtained by a series of mutations (flips) from the basis formed by the intervals in…