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It is difficult to tell if there is a Condorcet spanning tree
1Institute of Public Economics, University of Graz, Graz, Austria.
Mathematical Methods of Operations Research (Heidelberg, Germany)
|August 27, 2016
Summary
We extend the Condorcet criterion from voting theory to network design using spanning trees. Determining if a consensus network exists or if one meets the criterion is computationally intractable.
Area of Science:
- Computational Social Choice
- Graph Theory
- Network Design
Background:
- Decision-making in network installation often involves conflicting preferences.
- Spanning trees represent potential network structures.
- Group consensus on a single network is challenging.
Purpose of the Study:
- To adapt the Condorcet criterion for selecting a group spanning tree.
- To investigate the computational complexity of finding a Condorcet winner spanning tree.
Main Methods:
- Applying the Condorcet criterion to pairwise comparisons of spanning trees.
- Defining 'closeness' between spanning trees using set difference of edges.
- Analyzing the computational complexity of existence and verification problems.
Main Results:
- The existence of a spanning tree satisfying the Condorcet criterion is computationally intractable to determine.
- Verifying if a given spanning tree meets the Condorcet criterion is also computationally intractable.
Conclusions:
- The direct application of the Condorcet criterion to group spanning tree selection faces significant computational hurdles.
- New approaches may be needed for efficient consensus network design.
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