Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle
  Detection   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.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph