Abstract
In this paper, we survey some results, conjectures and open problems dealing with the combinatorial and algorithmic aspects of the linear ordering problem. This problem consists in finding a linear order which is at minimum distance from a (weighted or not) tournament. We show how it can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates to a collective ranking of these candidates.
| Original language | English |
|---|---|
| Pages (from-to) | 5-60 |
| Number of pages | 56 |
| Journal | 4OR |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2007 |
Keywords
- Acyclic subgraph
- Aggregation of preferences
- Complexity
- Feedback arc set
- Graph theory
- Kemeny's problem
- Linear ordering problem
- Median order
- Optimal triangulation
- Reversing set
- Slater's problem
- Social choice
- Tournament solutions
- Voting theory
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