Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection

Kaspars Balodis; Jānis Iraids

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arXiv · 1507.03885

Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection

Kaspars Balodis·Jānis Iraids

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Abstract

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 $f:V\rightarrow \{0,1\}$ as a black box. We are asked to determine if there exist $(u,v) \in E$, 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 ($\Omega(\sqrt{n})$ and $\Omega(n)$, respectively) and there is no known matching upper bound.

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Kaspars Balodis, Jānis Iraids. 2015-07-14. Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection. https://arxiv.org/abs/1507.03885

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