Related papers: On the extension complexity of scheduling
Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The…
We consider the following shared-resource scheduling problem: Given a set of jobs $J$, for each $j\in J$ we must schedule a job-specific processing volume of $v_j>0$. A total resource of $1$ is available at any time. Jobs have a resource…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of $2$ and $\min\{m-k+1,…
Malleable scheduling is a model that captures the possibility of parallelization to expedite the completion of time-critical tasks. A malleable job can be allocated and processed simultaneously on multiple machines, occupying the same time…
We consider the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities where each job can only be processed on a specified subset of machines called its processing set. For the case of…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a…
We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
We consider composition orderings for linear functions of one variable. Given $n$ linear functions $f_1,\dots,f_n$ and a constant $c$, the objective is to find a permutation $\sigma$ that minimizes/maximizes $f_{\sigma(n)}\circ\dots\circ…
We consider the problem of scheduling a set of $n$ tasks on $m$ processors under precedence, communication, and global system energy constraints to minimize makespan. We extend existing scheduling models to account for energy usage and give…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
In the scheduling with non-uniform communication delay problem, the input is a set of jobs with precedence constraints. Associated with every precedence constraint between a pair of jobs is a communication delay, the time duration the…
We study the classic problem of scheduling $n$ precedence constrained unit-size jobs on $m = O(1)$ machines so as to minimize the makespan. In a recent breakthrough, Levey and Rothvoss \cite{LR16} developed a $(1+\epsilon)$-approximation…
We consider the $\mathcal{NP}$-hard problem $\mathrm{P} \mathbf{\vert} \mathrm{pmtn, setup=s_i} \mathbf{\vert} \mathrm{C_{\max}}$, the problem of scheduling $n$ jobs, which are divided into $c$ classes, on $m$ identical parallel machines…