Related papers: Lawler-Moore Speedups via Additive Combinatorics

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…

Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

The Linear Assignment Problem (LAP) is a fundamental combinatorial optimization task with applications ranging from computer vision to logistics. Classical exact solvers such as the Hungarian and Jonker-Volgenant (LAPJV) algorithms…

Large Language Models (LLMs) with Mixture-of-Expert (MoE) architectures achieve superior model performance with reduced computation costs, but at the cost of high memory capacity and bandwidth requirements. Near-Memory Processing (NMP)…

We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…

Subset sum is a very old and fundamental problem in theoretical computer science. In this problem, $n$ items with weights $w_1, w_2, w_3, \ldots, w_n$ are given as input and the goal is to find out if there is a subset of them whose weights…

The increasing size of large language models (LLMs) has led to a surge in memory requirements during training, often exceeding the capacity of high-bandwidth memory (HBM). Swap-based memory optimization incurs neither accuracy loss nor…

We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same…

In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…

In this paper we introduce the concept of additive approximation schemes and apply it to load balancing problems. Additive approximation schemes aim to find a solution with an absolute error in the objective of at most $\epsilon h$ for some…

Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…

Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various…

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…

Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

Speculative decoding accelerates LLM inference by having a lightweight draft model propose speculative windows of candidate tokens for parallel verification by a larger target model. In practice, speculative efficiency is often bottlenecked…

We consider a parallel computational model that consists of $P$ processors, each with a fast local ephemeral memory of limited size, and sharing a large persistent memory. The model allows for each processor to fault with bounded…