A quantum query algorithm for the graph collision problem [article]

Dmitry Gavinsky, Tsuyoshi Ito
2012 arXiv   pre-print
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is O(sqrt(n)+sqrt(alpha*(G))), where n is the number of vertices and alpha*(G) is the maximum total degree of the vertices in an independent set of G. Notably, if G is a random graph where every edge is present with a fixed probability independently of other edges,
more » ... hen our algorithm requires O(sqrt(n log n)) queries on most graphs, which is optimal up to the sqrt(log n) factor on most graphs.
arXiv:1204.1527v1 fatcat:o44qph5yrvdx7pagl35ivsirnu