Integer programming in parameterized complexity: Five miniatures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453167" target="_blank" >RIV/00216208:11320/22:10453167 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11620/22:10453167 RIV/68407700:21240/22:00343692

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=T5-dd7eCd2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=T5-dd7eCd2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disopt.2020.100596" target="_blank" >10.1016/j.disopt.2020.100596</a>

Result language

angličtina

Original language name

Integer programming in parameterized complexity: Five miniatures

Original language description

Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra&apos;s algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community of the strengths and limitations of the available tools. This is understandable: it is often difficult to infer exact runtimes or even the distinction between FPT and XP algorithms, and some knowledge is simply unwritten folklore in a different community. We wish to make a step in remedying this situation. To that end, we first provide an easy to navigate quick reference guide of integer programming algorithms from the perspective of parameterized complexity. Then, we show their applications in three case studies, obtaining FPT algorithms with runtime f (k)poly(n). We focus on: Modeling: since the algorithmic results follow by applying existing algorithms to new models, we shift the focus from the complexity result to the modeling result, highlighting common patterns and tricks which are used. Optimality program: after giving an FPT algorithm, we are interested in reducing the dependence on the parameter; we show which algorithms and tricks are often useful for speed-ups. Minding the poly(n): reducing f (k) often has the unintended consequence of increasing poly(n); so we highlight the common trade-offs and show how to get the best of both worlds. Specifically, we consider graphs of bounded neighborhood diversity which are in a sense the simplest of dense graphs, and we show several FPT algorithms for Capacitated Dominating Set, Sum Coloring, Max-q-Cut, and certain other coloring problems by modeling them as convex programs in fixed dimension, n-fold integer programs, bounded dual treewidth programs, indefinite quadratic programs in fixed dimension, parametric integer programs in fixed dimension, and 2-stage stochastic integer programs. (C) 2020 TheAuthor(s). Published by Elsevier B.V.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

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

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2022

Confidentiality

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

Name of the periodical

Discrete Optimization

ISSN

1572-5286

e-ISSN

1873-636X

Volume of the periodical

44

Issue of the periodical within the volume

P1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

33

Pages from-to

100596

UT code for WoS article

000832713200004

EID of the result in the Scopus database

2-s2.0-85088118525