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An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem

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1 Author(s)
Pettie, S. ; Dept. of Comput. Sci., Texas Univ., Austin, TX, USA

We consider the problem of preprocessing an edge-weighted tree T in order to quickly answer queries of the following type: does a given edge e belong in the minimum spanning tree of T ∪ {e}? Whereas the offline minimum spanning tree verification problem admits a lovely linear time solution, we demonstrate an inherent inverse-Ackermann type tradeoff in the online MST verification problem. In particular, any scheme that answers queries in t comparisons must invest Ω(n log λt (n)) time preprocessing the tree, where λt is the inverse of the tth row of Ackermann's function. This implies a query lower bound of Ω(α(n)) for the case of linear preprocessing time. We also show that our lower bound is tight to within a factor of 2 in the t parameter.

Published in:

Foundations of Computer Science, 2002. Proceedings. The 43rd Annual IEEE Symposium on

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