Parameterized Complexity of Minimum Membership Dominating Set
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00374506" target="_blank" >RIV/68407700:21240/23:00374506 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00453-023-01139-7" target="_blank" >https://doi.org/10.1007/s00453-023-01139-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00453-023-01139-7" target="_blank" >10.1007/s00453-023-01139-7</a>
Alternative languages
Result language
angličtina
Original language name
Parameterized Complexity of Minimum Membership Dominating Set
Original language description
Given a graph G = (V, E) and an integer k, the Minimum Membership Dominating Set (MMDS) problem seeks to find a dominating set S subset of V of G such that for each v is an element of V, vertical bar N[v] boolean AND S vertical bar is at most k. We investigate the parameterized complexity of the problem and obtain the following results for the MMDS problem. First, we show that the MMDS problem is NP-hard even on planar bipartite graphs. Next, we show that the MMDS problem is W[1]-hard for the parameter pathwidth (and thus, for treewidth) of the input graph. Then, for split graphs, we show that the MMDS problem is W[2]-hard for the parameter k. Further, we complement the pathwidth lower bound by an FPT algorithm when parameterized by the vertex cover number of input graph. In particular, we design a 2(O(vc))vertical bar V vertical bar(O(1)) time algorithm for the MMDS problem where vc is the vertex cover number of the input graph. Finally, we show that the running time lower bound based on ETH is tight for the vertex cover parameter.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algorithmica
ISSN
0178-4617
e-ISSN
1432-0541
Volume of the periodical
85
Issue of the periodical within the volume
11
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
3430-3452
UT code for WoS article
001010001200001
EID of the result in the Scopus database
2-s2.0-85163100740