Scheduling meets n-fold integer programming

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10386756" target="_blank" >RIV/00216208:11320/18:10386756 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10951-017-0550-0" target="_blank" >https://doi.org/10.1007/s10951-017-0550-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10951-017-0550-0" target="_blank" >10.1007/s10951-017-0550-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Scheduling meets n-fold integer programming

Popis výsledku v původním jazyce

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. In this paper, we continue this study and show that several additional cases of fundamental scheduling problems are fixed-parameter tractable for some natural parameters. Our main tool is n-fold integer programming, a recent variable dimension technique which we believe to be highly relevant for the parameterized complexity community. This paper serves to showcase and highlight this technique. Specifically, we show the following four scheduling problems to be fixed-parameter tractable, where pmax is the maximum processing time of a job and wmax is the maximum weight of a job: Makespan minimization on uniformly related machines (Q parallel to C-max) parameterized by p(max), Makespan minimization on unrelated machines (R parallel to C-max) parameterized by pmax and the number of kinds of machines (defined later), Sum of weighted completion times minimization on unrelated machines parameterized by pmax + wmax and the number of kinds of machines, The same problem, parameterized by the number of distinct job times and the number of machines.

Název v anglickém jazyce

Scheduling meets n-fold integer programming

Popis výsledku anglicky

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. In this paper, we continue this study and show that several additional cases of fundamental scheduling problems are fixed-parameter tractable for some natural parameters. Our main tool is n-fold integer programming, a recent variable dimension technique which we believe to be highly relevant for the parameterized complexity community. This paper serves to showcase and highlight this technique. Specifically, we show the following four scheduling problems to be fixed-parameter tractable, where pmax is the maximum processing time of a job and wmax is the maximum weight of a job: Makespan minimization on uniformly related machines (Q parallel to C-max) parameterized by p(max), Makespan minimization on unrelated machines (R parallel to C-max) parameterized by pmax and the number of kinds of machines (defined later), Sum of weighted completion times minimization on unrelated machines parameterized by pmax + wmax and the number of kinds of machines, The same problem, parameterized by the number of distinct job times and the number of machines.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Scheduling

ISSN

1094-6136

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

493-503

Kód UT WoS článku

000444590500002

EID výsledku v databázi Scopus

2-s2.0-85030569513