Related papers: Exact and Approximate High-Multiplicity Scheduling…
Consider a high-multiplicity Bin Packing instance $I$ with $d$ distinct item types. In 2014, Goemans and Rothvoss gave an algorithm with runtime ${{|I|}^2}^{O(d)}$ for this problem~[SODA'14], where $|I|$ denotes the encoding length of the…
We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs executed before a common due date. By preprocessing and constructing an auxiliary…
We study the classical scheduling problem of minimizing the makespan of a set of unit size jobs with precedence constraints on parallel identical machines. Research on the problem dates back to the landmark paper by Graham from 1966 who…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH) 1. The scheduling problem on a constant number $m$ of…
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…
In parallel machine scheduling, we are given a set of jobs, together with a number of machines and our goal is to decide for each job, when and on which machine(s) it should be scheduled in order to minimize some objective function.…
The NP-hard scheduling problem P||C_max encompasses a set of tasks with known execution time which must be mapped to a set of identical machines such that the overall completion time is minimized. In this work, we improve existing…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
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…
This paper studies the non-preemptive single-machine scheduling problem with heterogeneous release times and processing times, with the objective of minimizing total waiting time. The problem is known to be NP-hard. By modeling machine idle…
Let $d$ be a positive integer. For a finite set $X \subseteq \mathbb{R}^d$, we define its integer cone as the set $\mathsf{IntCone}(X) := \{ \sum_{x \in X} \lambda_x \cdot x \mid \lambda_x \in \mathbb{Z}_{\geq 0} \} \subseteq \mathbb{R}^d$.…
A central problem in scheduling is to schedule $n$ unit size jobs with precedence constraints on $m$ identical machines so as to minimize the makespan. For $m=3$, it is not even known if the problem is NP-hard and this is one of the last…
Makespan minimization (on parallel identical or unrelated machines) is arguably the most natural and studied scheduling problem. A common approach in practical algorithm design is to reduce the size of a given instance by a fast…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is…
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.…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
In breakthrough work, Tardos (Oper. Res. '86) gave a proximity based framework for solving linear programming (LP) in time depending only on the constraint matrix in the bit complexity model. In Tardos's framework, one reduces solving the…
We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…