Tight Lower Bounds for Block-Structured Integer Programs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493491" target="_blank" >RIV/00216208:11320/24:10493491 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-59835-7_17" target="_blank" >https://doi.org/10.1007/978-3-031-59835-7_17</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-59835-7_17" target="_blank" >10.1007/978-3-031-59835-7_17</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tight Lower Bounds for Block-Structured Integer Programs

Popis výsledku v původním jazyce

We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their constraint matrix yields multi-stage IPs. The state-of-the-art algorithms to solve these IPs have an exponential gap in their running times, making it natural to ask whether this gap is inherent. We answer this question affirmative. Assuming the Exponential Time Hypothesis, we prove lower bounds showing that the exponential difference is necessary, and that the known algorithms are near optimal. Moreover, we prove unconditional lower bounds on the norms of the Graver basis, a fundamental building block of all known algorithms to solve these IPs. This shows that none of the current approaches can be improved beyond this bound.

Název v anglickém jazyce

Tight Lower Bounds for Block-Structured Integer Programs

Popis výsledku anglicky

We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their constraint matrix yields multi-stage IPs. The state-of-the-art algorithms to solve these IPs have an exponential gap in their running times, making it natural to ask whether this gap is inherent. We answer this question affirmative. Assuming the Exponential Time Hypothesis, we prove lower bounds showing that the exponential difference is necessary, and that the known algorithms are near optimal. Moreover, we prove unconditional lower bounds on the norms of the Graver basis, a fundamental building block of all known algorithms to solve these IPs. This shows that none of the current approaches can be improved beyond this bound.

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)

Projekt

<a href="/cs/project/GA22-22997S" target="_blank" >GA22-22997S: Efektivní a realistické modely ve výpočetní teorii voleb</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, IPCO 2024

ISBN

978-3-031-59834-0

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

14

Strana od-do

224-237

Název nakladatele

SPRINGER INTERNATIONAL PUBLISHING AG

Místo vydání

CHAM

Místo konání akce

Wroclaw

Datum konání akce

3. 7. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001275732800017