Integer Programming in ParameterizedComplexity: Three Miniatures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00328404" target="_blank" >RIV/68407700:21240/19:00328404 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21240/19:00334324

Result on the web

<a href="http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=10222" target="_blank" >http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=10222</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.IPEC.2018.21" target="_blank" >10.4230/LIPIcs.IPEC.2018.21</a>

Result language

angličtina

Original language name

Integer Programming in ParameterizedComplexity: Three 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’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 application sin 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, and Max-q-Cut by modeling them as convex programs in fixed dimension,n-fold integer programs, bounded dual treewidth programs, and indefinite quadratic programs in fixed dimension.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Article name in the collection

13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

ISBN

978-3-95977-084-2

ISSN

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e-ISSN

1868-8969

Number of pages

16

Pages from-to

"21:1"-"21:16"

Publisher name

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Place of publication

Dagstuhl

Event location

Helsinky

Event date

Aug 22, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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