---
title: "Kemeny Elections with Bounded Single-Peaked or Single-Crossing Width"
authors:
  - "Denis Cornaz"
  - "Lucie Galand"
  - "Olivier Spanjaard"
doi: ""
url: "https://ijcai.org/proceedings/2013/23"
pdf: "https://ijcai.org/proceedings/2013/0023.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "76-81"
track: ""
keywords:
---

# Kemeny Elections with Bounded Single-Peaked or Single-Crossing Width

Denis Cornaz, Lucie Galand, Olivier Spanjaard

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 76-81.

## Abstract

This paper is devoted to complexity results regarding specific measures of proximity to single-peakedness and single-crossingness, called single-peaked width [Cornaz et al., 2012] and single-crossing width. Thanks to the use of the PQ-tree data structure [Booth and Lueker, 1976], we show that both problems are polynomial time solvable in the general case (while it was only known for single-peaked width and in the case of narcissistic preferences). Furthermore, we establish one of the first results (to our knowledge) concerning the effect of nearly single-peaked electorates on the complexity of an NP-hard voting system, namely we show the fixed-parameter tractability of Kemeny elections with respect to the parameters single-peaked width and single-crossing width.