Related papers: Solving MaxSAT with Matrix Multiplication

Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…

In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the…

The Max-k-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic NP-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-k-Cut, they often lack guarantees of…

Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision problem that is known to be NP-hard. In this paper, we compare LightSolver's quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT problem.…

A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single computation task and batch processing of multiple distinct computation tasks. While these works…

Multi-Chip-Modules (MCMs) reduce the design and fabrication cost of machine learning (ML) accelerators while delivering performance and energy efficiency on par with a monolithic large chip. However, ML compilers targeting MCMs need to…

The efficient scheduling of multi-task jobs across multiprocessor systems has become increasingly critical with the rapid expansion of computational systems. This challenge, known as Multiprocessor Multitask Scheduling (MPMS), is essential…

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…

The Unbalanced Optimal Transport (UOT) problem plays increasingly important roles in computational biology, computational imaging and deep learning. Scaling algorithm is widely used to solve UOT due to its convenience and good convergence…

Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem.…

We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to…

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…

The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

Resilient submodular maximization refers to the combinatorial problems studied by Nemhauser and Fisher and asks how to maximize an objective given a number of adversarial removals. For example, one application of this problem is multi-robot…

Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the bounded job start scheduling problem. Given a set of jobs, each…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…