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Integer Programming in Parameterized Complexity: Three Miniatures

Identifikátory výsledku

  • Kód výsledku v IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00334324" target="_blank" >RIV/68407700:21240/19:00334324 - isvavai.cz</a>

  • Výsledek na webu

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

Alternativní jazyky

  • Jazyk výsledku

    angličtina

  • Název v původním jazyce

    Integer Programming in Parameterized Complexity: Three Miniatures

  • Popis výsledku v původním jazyce

    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 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, 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.

  • Název v anglickém jazyce

    Integer Programming in Parameterized Complexity: Three Miniatures

  • Popis výsledku anglicky

    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 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, 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.

Klasifikace

  • Druh

    D - Stať ve sborníku

  • CEP obor

  • OECD FORD obor

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

Návaznosti výsledku

  • Projekt

  • Návaznosti

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Ostatní

  • Rok uplatnění

    2019

  • Kód důvěrnosti údajů

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

Údaje specifické pro druh výsledku

  • Název statě ve sborníku

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

  • ISBN

    978-3-95977-084-2

  • ISSN

  • e-ISSN

    1868-8969

  • Počet stran výsledku

    16

  • Strana od-do

    "21:1"-"21:16"

  • Název nakladatele

    Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

  • Místo vydání

    Dagstuhl

  • Místo konání akce

    Helsinky

  • Datum konání akce

    22. 8. 2018

  • Typ akce podle státní příslušnosti

    WRD - Celosvětová akce

  • Kód UT WoS článku