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18 April 2024
 
  » arxiv » 1109.5135

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A learning graph based quantum query algorithm for finding constant-size subgraphs
Troy Lee ; Frederic Magniez ; Miklos Santha ;
Date 23 Sep 2011
AbstractWe use the learning graph framework of Belovs to show that the quantum query complexity of determining if an $n$-vertex graph contains a fixed $k$-vertex subgraph $H$ is $O(n^{2-2/k-t})$ where $t=(2k-d-3)/(k(d+1)(m+2))$ and $d$ and $m$ are such that $H$ has a vertex of degree $d$ and $m+d$ edges. The previous best algorithm of Magniez et al. had complexity $widetilde O(n^{2-2/k})$.
Source arXiv, 1109.5135
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