Related papers: On the extension complexity of scheduling
Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines…
We present a simple transformation of any linear program or semidefinite program into an equivalent convex optimization problem whose only constraints are linear equations. The objective function is defined on the whole space, making…
Online scheduling has been a well studied and challenging research problem over the last five decades since the pioneering work of Graham with immense practical significance in various applications such as interactive parallel processing,…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time…
In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings.…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Large language models (LLMs) are increasingly explored for their reasoning capabilities, yet their ability to perform structured, constraint-based optimization from natural language remains insufficiently understood. This study evaluates…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…
A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
The dictionary matching problem is to locate occurrences of any pattern among a set of patterns in a given text. Massive data sets abound and at the same time, there are many settings in which working space is extremely limited. We…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
Reducing the cognitive complexity of a piece of code to a given threshold is not trivial. Recently, we modeled software cognitive complexity reduction as an optimization problem and we proposed an approach to assist developers on this task.…
We consider the minimum makespan problem for $n$ tasks and two unrelated parallel selfish machines. Let $R_n$ be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms…
We are concerned with the problem of scheduling $n$ jobs onto $m$ identical machines. Each machine has to be in operation for a prescribed time, and the objective is to minimize the total machine working time. Precisely, let $c_i$ be the…
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…