Kernelization of graph hamiltonicity: Proper H-graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00334116" target="_blank" >RIV/68407700:21240/19:00334116 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/19:10404857

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-030-24766-9_22" target="_blank" >http://dx.doi.org/10.1007/978-3-030-24766-9_22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-24766-9_22" target="_blank" >10.1007/978-3-030-24766-9_22</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 Biró, 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(formula presented), that is, we design an algorithm that for an n-vertex graph G and an integer k>= 1, in time polynomial in n and (formula presented), outputs a graph G' of size (formula presented) and k'<= | V(G') | such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G' is coverable by k' vertex-disjoint paths.Cycle Cover admits a compression of size (formula presented) into another problem, called Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and (formula presented), outputs an equivalent instance of Prize Collecting Cycle Cover of size (formula presented). 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 Biró, 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(formula presented), that is, we design an algorithm that for an n-vertex graph G and an integer k>= 1, in time polynomial in n and (formula presented), outputs a graph G' of size (formula presented) and k'<= | V(G') | such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G' is coverable by k' vertex-disjoint paths.Cycle Cover admits a compression of size (formula presented) into another problem, called Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and (formula presented), outputs an equivalent instance of Prize Collecting Cycle Cover of size (formula presented). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.

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/GA17-20065S" target="_blank" >GA17-20065S: Těsné parametrizované výsledky pro problémy orientované souvislosti</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

16th International Symposium on Algorithms and Data Structures (WADS 2019)

ISBN

978-3-030-24765-2

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

15

Strana od-do

296-310

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Edmonton

Datum konání akce

5. 8. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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