Randomized algorithms
Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
On finding a minimum spanning tree in a network with random weights
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Random Structures & Algorithms
Online computation and competitive analysis
Online computation and competitive analysis
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
A new average case analysis for completion time scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Predicting the labels of an unknown graph via adaptive exploration
Theoretical Computer Science
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This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniformly distributed over [0,1]. An algorithm receives the edges one by one and has to decide immediately whether to include the current edge into the spanning tree or to reject it. The corresponding edge sequence is determined by some adversary. We propose an algorithm which achieves $\mathbb{E}[ALG]/\mathbb{E}[OPT]=O(1)$ and $\mathbb{E}[ALG/OPT]=O(1)$ against a fair adaptive adversary, i.e., an adversary which determines the edge order online and is fair in a sense that he does not know more about the edge weights than the algorithm. Furthermore, we prove that no online algorithm performs better than $\mathbb{E}[ALG]/\mathbb{E}[OPT]=\Omega(\log n)$ if the adversary knows the edge weights in advance. This lower bound is tight, since there is an algorithm which yields $\mathbb{E}[ALG]/\mathbb{E}[OPT]=O(\log n)$ against the strongest-imaginable adversary.