  Hypervolume indicator is a commonly accepted quality measure for comparing
Pareto approximation set generated by multi-objective optimizers. The best
known algorithm to calculate it for $n$ points in $d$-dimensional space has a
run time of $O(n^{d/2})$ with special data structures. This paper presents a
recursive, vertex-splitting algorithm for calculating the hypervolume indicator
of a set of $n$ non-comparable points in $d>2$ dimensions. It splits out
multiple child hyper-cuboids which can not be dominated by a splitting
reference point. In special, the splitting reference point is carefully chosen
to minimize the number of points in the child hyper-cuboids. The complexity
analysis shows that the proposed algorithm achieves $O((\frac{d}{2})^n)$ time
and $O(dn^2)$ space complexity in the worst case.
