In this paper, we will propose a universal relation between the holographiccomplexity (dual to a volume in AdS) and the holographic entanglement entropy(dual to an area in AdS). We will explicitly demonstrate that our conjuncturehold for all a metric asymptotic to AdS$_3$, and then argue that such arelation should hold in general due to the AdS version of the Cavalieriprinciple. We will demonstrate that it holds for Janus solution, which havebeen recently been obtained in type IIB string theory. We will also show thatthis conjecture holds for a circular disk. This conjecture will be used to showthat the proposal that the complexity equals action, and the proposal that thecomplexity equal volume can represent the same physics. Thus, using thisconjecture, we will show that the black holes are fastest computers, using theproposal that complexity equals volume.
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