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Minimum Spanning Tree Verification Under Uncertainty

  • Thomas Erlebach
  • Michael HoffmannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

Abstract

In the verification under uncertainty setting, an algorithm is given, for each input item, an uncertainty area that is guaranteed to contain the exact input value, as well as an assumed input value. An update of an input item reveals its exact value. If the exact value is equal to the assumed value, we say that the update verifies the assumed value. We consider verification under uncertainty for the minimum spanning tree (MST) problem for undirected weighted graphs, where each edge is associated with an uncertainty area and an assumed edge weight. The objective of an algorithm is to compute the smallest set of updates with the property that, if the updates of all edges in the set verify their assumed weights, the edge set of an MST can be computed. We give a polynomial-time optimal algorithm for the MST verification problem by relating the choices of updates to vertex covers in a bipartite auxiliary graph. Furthermore, we consider an alternative uncertainty setting where the vertices are embedded in the plane, the weight of an edge is the Euclidean distance between the endpoints of the edge, and the uncertainty is about the location of the vertices. An update of a vertex yields the exact location of that vertex. We prove that the MST verification problem in this vertex uncertainty setting is NP-hard. This shows a surprising difference in complexity between the edge and vertex uncertainty settings of the MST verification problem.

Keywords

Bipartite Graph Planar Graph Minimum Span Tree Online Algorithm Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The second author would like to thank the University of Leicester for supporting this research in granting him academic study leave.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LeicesterLeicesterUK

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