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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2011.661
URN: urn:nbn:de:0030-drops-30521
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3052/
Childs, Andrew M. ;
Kothari, Robin
Quantum query complexity of minor-closed graph properties
Abstract
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties -- those that cannot be characterized by a finite set of forbidden subgraphs -- have quantum query complexity Theta(n^(3/2)). To establish this, we prove an adversary lower bound using a detailed analysis of the structure of minor-closed properties with respect to forbidden topological minors and forbidden subgraphs. On the other hand, we show that minor-closed properties (and more generally, sparse graph properties) that can be characterized by finitely many forbidden subgraphs can be solved strictly faster, in o(n^(3/2)) queries. Our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph-finding problems.
BibTeX - Entry
@InProceedings{childs_et_al:LIPIcs:2011:3052,
author = {Andrew M. Childs and Robin Kothari},
title = {{Quantum query complexity of minor-closed graph properties}},
booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
pages = {661--672},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-25-5},
ISSN = {1868-8969},
year = {2011},
volume = {9},
editor = {Thomas Schwentick and Christoph D{\"u}rr},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3052},
URN = {urn:nbn:de:0030-drops-30521},
doi = {10.4230/LIPIcs.STACS.2011.661},
annote = {Keywords: quatum query complexity, quantum algorithms, lower bounds, graph minors, graph properties}
}
Keywords: |
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quatum query complexity, quantum algorithms, lower bounds, graph minors, graph properties |
Collection: |
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28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) |
Issue Date: |
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2011 |
Date of publication: |
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11.03.2011 |