Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time - Czumaj, Artur; Sohler, Christian (SIAM journal on computing, 2009)
In this paper the authors present a sublinear-time (1+...)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is ... Since the full description of an n-point metric space is of size ..., the complexity of their algorithm is sublinear with respect to the input size. Their algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. They also show that no deterministic algorithm can achieve a B-approximation in ... time. Furthermore, it has been previously shown that no o(n^sup 2^) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum. (ProQuest: ... denotes formulae/symbols omitted.)