Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection [article]

Kaspars Balodis, Jānis Iraids
2015 arXiv   pre-print
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access to a graph (V,E) and access to a function f:V→{0,1} as a black box. We are asked to determine if there exist (u,v) ∈ E, such that f(u)=f(v)=1. In TRIANGLE we have a black box access to an adjacency matrix of a graph and we have to determine if the
more » ... raph contains a triangle. For both of these problems the known lower bounds are trivial (Ω(√(n)) and Ω(n), respectively) and there is no known matching upper bound.
arXiv:1507.03885v1 fatcat:m7gwpzsbcnc5rbsbvjd4dlag3i