Even Delta-Matroids and the Complexity of Planar Boolean CSPs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401293" target="_blank" >RIV/00216208:11320/19:10401293 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Uv7NvVpnov" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Uv7NvVpnov</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3230649" target="_blank" >10.1145/3230649</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Even Delta-Matroids and the Complexity of Planar Boolean CSPs

Popis výsledku v původním jazyce

The main result of this article is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Delta-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Using a reduction to even Delta-matroids, we then extend the tractability result to larger classes of Delta-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely, co-independent, compact, local, linear, and binary, with the following caveat: We represent Delta-matroids by lists of tuples, while the last two use a representation by matrices. Since an n x n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Delta-matroids.

Název v anglickém jazyce

Even Delta-Matroids and the Complexity of Planar Boolean CSPs

Popis výsledku anglicky

The main result of this article is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Delta-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Using a reduction to even Delta-matroids, we then extend the tractability result to larger classes of Delta-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely, co-independent, compact, local, linear, and binary, with the following caveat: We represent Delta-matroids by lists of tuples, while the last two use a representation by matrices. Since an n x n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Delta-matroids.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

ACM Transactions on Algorithms

ISSN

1549-6325

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

33

Strana od-do

22

Kód UT WoS článku

000468036500007

EID výsledku v databázi Scopus

2-s2.0-85061215080