Table 3 VCP algorithms and their complexities

VCP ^3,r,d (Naïve)

$O\left(\left|V\right|log\left(\frac{\left|E\right|}{\left|V\right|}\right)\right)$

VCP ^3,r,d

$O\left(\frac{\left|E\right|}{\left|V\right|}\right)$

VCP ^4,r,d (Naïve)

$O\left(|V{|}^{2}log\frac{\left|E\right|}{\left|V\right|}\right)$

VCP ^4,r,d (Improved)

$O\left({\left(\frac{\left|E\right|}{\left|V\right|}\right)}^{2}log\frac{\left|E\right|}{\left|V\right|}\right)$

VCP ^4,r,d

$O\left({\left(\frac{\left|E\right|}{\left|V\right|}\right)}^2\right)$

VCP ^n,r,d

$\mathrm{\Omega }\left({\left(\frac{\left|E\right|}{\left|V\right|}\right)}^{n-2}\right)$