An Inverse-Ackermann Style Lower Bound for the Online Minimum Spanning Tree

An Inverse-Ackermann Style Lower Bound for the Online Minimum Spanning Tree Verification Problem

We consider the problem of preprocessing an edgeweighted tree in order to quickly answer queries of the following type: does a given edge belong in the minimum spanning tree of ? Whereas the offline minimum spanning tree verification problem admits a lovely linear time solution, we demonstrate an inherent inverseAckermann type tradeoff in the online MST verification problem. In particular, any ...

An Inverse-Ackermann Type Lower Bound For Online Minimum Spanning Tree Verification

Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST (G). A celebrated result of Komlós shows that this problem can be solved with a linear number of comparisons. Somewhat unexpectedly, MST verification turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to w...

An Inverse-A kermann Type Lower Bound for Online Minimum Spanning Tree Veri ation

Sensitivity Analysis of Minimum Spanning Trees in Sub-inverse-Ackermann Time

We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(m logα(m,n)) time, where α is the inverse-Ackermann function. This improves upon a long standing bound of O(mα(m,n)) established by Tarjan. Our algorithms are based on an efficient split-findmin data structure, which maintains a collection of sequences of weighted eleme...

Finding Minimum Spanning Trees in O(m (m;n)) Time

We describe a deterministic minimum spanning tree algorithm running in time O(m (m; n)), where is a natural inverse of Ackermann's function and m and n are the number of edges and vertices, respectively. This improves upon the O(m (m; n) log (m; n)) bound established by Chazelle in 1997. A similar O(m (m; n))-time algorithm was discovered independently by Chazelle, predating the algorithm prese...