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A quantum query algorithm for the graph collision problem
[article]

2012
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arXiv
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pre-print

We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is O(sqrt(n)+sqrt(alpha*(G))), where n is the number of vertices and alpha*(G) is the maximum total degree of the vertices in an independent set of G. Notably, if G is a random graph where every edge is present with a fixed probability independently of other edges,

arXiv:1204.1527v1
fatcat:o44qph5yrvdx7pagl35ivsirnu