Kernelization of Graph Hamiltonicity: Proper H-Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10439055" target="_blank" >RIV/00216208:11320/21:10439055 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21240/21:00350652

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wQHkVTwu2J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wQHkVTwu2J</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/19M1299001" target="_blank" >10.1137/19M1299001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Kernelization of Graph Hamiltonicity: Proper H-Graphs

Popis výsledku v původním jazyce

We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization is strongly influenced by the work of Bir&apos;o, Hujter, and Tuza, who in 1992 introduced H-graphs, intersection graphs of connected subgraphs of a subdivision of a fixed (multi-)graph H. In this work, we turn to proper H-graphs, where the containment relationship between the representations of the vertices is forbidden. As the treewidth of a graph measures how similar the graph is to a tree, the size of graph H is the parameter measuring the closeness of the graph to a proper interval graph. We prove the following results. Path Cover admits a kernel of size O (parallel to H parallel to(8)), where parallel to H parallel to is the size of graph H. In other words, we design an algorithm that for an n-vertex graph G and integer k geq 1, in time polynomial in n and parallel to H parallel to, outputs a graph Gprime of size scrO (parallel to H parallel to(8)) and kprime leq | V (G&apos; such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G&apos; is coverable by k&apos; vertex-disjoint paths. Hamiltonian Cycle admits a kernel of size O (parallel to H parallel to(8)). Cycle Cover admits a polynomial kernel. We prove it by providing a compression of size O (parallel to H parallel to(10)) into another NP-complete problem, namely, Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and parallel to H parallel to, outputs an equivalent instance of Prize Collecting Cycle Cover of sizeO (parallel to H parallel to(10)). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.

Název v anglickém jazyce

Kernelization of Graph Hamiltonicity: Proper H-Graphs

Popis výsledku anglicky

We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization is strongly influenced by the work of Bir&apos;o, Hujter, and Tuza, who in 1992 introduced H-graphs, intersection graphs of connected subgraphs of a subdivision of a fixed (multi-)graph H. In this work, we turn to proper H-graphs, where the containment relationship between the representations of the vertices is forbidden. As the treewidth of a graph measures how similar the graph is to a tree, the size of graph H is the parameter measuring the closeness of the graph to a proper interval graph. We prove the following results. Path Cover admits a kernel of size O (parallel to H parallel to(8)), where parallel to H parallel to is the size of graph H. In other words, we design an algorithm that for an n-vertex graph G and integer k geq 1, in time polynomial in n and parallel to H parallel to, outputs a graph Gprime of size scrO (parallel to H parallel to(8)) and kprime leq | V (G&apos; such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G&apos; is coverable by k&apos; vertex-disjoint paths. Hamiltonian Cycle admits a kernel of size O (parallel to H parallel to(8)). Cycle Cover admits a polynomial kernel. We prove it by providing a compression of size O (parallel to H parallel to(10)) into another NP-complete problem, namely, Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and parallel to H parallel to, outputs an equivalent instance of Prize Collecting Cycle Cover of sizeO (parallel to H parallel to(10)). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

35

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

53

Strana od-do

840-892

Kód UT WoS článku

000674142200010

EID výsledku v databázi Scopus

2-s2.0-85105713363