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Circuit cutting is a promising technique that leverages both quantum and classical computational resources, enabling the practical execution of large quantum circuits on noisy intermediate-scale quantum (NISQ) hardware. Recent approaches…
Take a prime power $q$, an integer $n\geq 2$, and a coordinate subspace $S\subseteq GF(q)^n$ over the Galois field $GF(q)$. One can associate with $S$ an $n$-partite $n$-uniform clutter $\mathcal{C}$, where every part has size $q$ and there…
In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space…
A partial combinatory algebra (PCA) is a set equipped with a partial binary operation that models a notion of computability. This paper studies a generalization of PCAs, introduced by W. Stekelenburg, where a PCA is not a set but an object…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…
In this paper, we describe Compact-Table (CT), a bitwise algorithm to enforce Generalized Arc Consistency (GAC) on table con- straints. Although this algorithm is the default propagator for table constraints in or-tools and OscaR, two…
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Protecting user privacy is a major concern for many machine learning systems that are deployed at scale and collect from a diverse set of population. One way to address this concern is by collecting and releasing data labels in an…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on…
This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…
The existing inverse power ($\mathbf{IP}$) method for solving the balanced graph cut lacks local convergence and its inner subproblem requires a nonsmooth convex solver. To address these issues, we develop a simple inverse power…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style…
Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be…
We present pure-integer Gomory cuts in a way so that they are derived with respect to a "dual form" pure-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. The input…
When partitioning gate-level netlists using graphs, it is beneficial to cluster gates to reduce the order of the graph and preserve some characteristics of the circuit that the partitioning might degrade. Gate clustering is even more…
We consider integer programs whose constraint matrix has a special block structure: $\min\{f(x):H_{com}x=b, l\le x\le u,x\in\mathbb{Z}^{t_B+nt_A}\}$, where the objective function $f$ is separable convex and the constraint matrix $H_ {com}$…
Modern computing workloads commonly involve matrix-matrix multiplication (mmul) as a core computing pattern. Coarse-Grained Reconfigurable Arrays (CGRAs) can flexibly and efficiently support it, since they combine operation-level…