IV-matching is strongly NP-hard

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10366352" target="_blank" >RIV/00216208:11320/17:10366352 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ipl.2017.04.014" target="_blank" >http://dx.doi.org/10.1016/j.ipl.2017.04.014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2017.04.014" target="_blank" >10.1016/j.ipl.2017.04.014</a>

Result language
angličtina
Original language name
IV-matching is strongly NP-hard
Original language description
IV-matching is a generalization of perfect bipartite matching. The complexity of finding IV-matching in a graph was posted as an open problem in [Fiala, Klavik, Kratochvil, Nedela, ICALP 2014]. It was shown that if it is possible to find an IV-matching in a polynomial time, then the described algorithm can be modified to run in polynomial time. In this note, we resolve the question and prove that, contrary to the expectations of the authors, the given problem is strongly NP-hard (already in the simplest non-trivial case of three layers). Hence it is unlikely that there would be an efficient (polynomial or pseudo polynomial in case of at least four layers) algorithm solving the problem.
Czech name
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Czech description
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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)

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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