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DOI: 10.4230/LIPIcs.ICALP.2020.49
URN: urn:nbn:de:0030-drops-124568
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12456/
Fomin, Fedor V. ; Lokshtanov, Daniel ; Mihajlin, Ivan ; Saurabh, Saket ; Zehavi, Meirav
Computation of Hadwiger Number and Related Contraction Problems: Tight Lower Bounds
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Abstract
We prove that the Hadwiger number of an n-vertex graph G (the maximum size of a clique minor in G) cannot be computed in time n^o(n), unless the Exponential Time Hypothesis (ETH) fails. This resolves a well-known open question in the area of exact exponential algorithms. The technique developed for resolving the Hadwiger number problem has a wider applicability. We use it to rule out the existence of n^o(n)-time algorithms (up to ETH) for a large class of computational problems concerning edge contractions in graphs.
BibTeX - Entry
@InProceedings{fomin_et_al:LIPIcs:2020:12456,
author = {Fedor V. Fomin and Daniel Lokshtanov and Ivan Mihajlin and Saket Saurabh and Meirav Zehavi},
title = {{Computation of Hadwiger Number and Related Contraction Problems: Tight Lower Bounds}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {49:1--49:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12456},
URN = {urn:nbn:de:0030-drops-124568},
doi = {10.4230/LIPIcs.ICALP.2020.49},
annote = {Keywords: Hadwiger Number, Exponential-Time Hypothesis, Exact Algorithms, Edge Contraction Problems}
}
| Keywords: | Hadwiger Number, Exponential-Time Hypothesis, Exact Algorithms, Edge Contraction Problems | |
| Seminar: | 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 29.06.2020 |
