TY - JOUR
T1 - Quantum query complexity of minor-closed graph properties
JF - Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011), Leibniz International Proceedings in Informatics
Y1 - 2011
A1 - Andrew M. Childs
A1 - Robin Kothari
AB - 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.
VL - 9
U4 - 661-672
UR - http://arxiv.org/abs/1011.1443v2
J1 - Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011)
U5 - 10.4230/LIPIcs.STACS.2011.661
ER -