%0 Journal Article
%J Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011), Leibniz International Proceedings in Informatics
%D 2011
%T Quantum query complexity of minor-closed graph properties
%A Andrew M. Childs
%A Robin Kothari
%X 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.
%B Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011), Leibniz International Proceedings in Informatics
%V 9
%P 661-672
%8 2011/01/01
%G eng
%U http://arxiv.org/abs/1011.1443v2
%! Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011)
%R 10.4230/LIPIcs.STACS.2011.661