Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection
Kaspars Balodis, Jānis Iraids · Baltic Journal of Modern Computing · 2016
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 graph 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.