Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of Kemeny elections
Theoretical Computer Science
Single-peaked consistency and its complexity
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
TreeMatrix: A Hybrid Visualization of Compound Graphs
Computer Graphics Forum
Stable matching with preferences derived from a psychological model
Operations Research Letters
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We study the complexity of electing a committee under several variants of the Chamberlin-Courant rule when the voters' preferences are single-peaked on a tree. We first show that this problem is easy for the egalitarian, or "minimax" version of this problem, for arbitrary trees and misrepresentation functions. For the standard (utilitarian) version of this problem we provide an algorithm for an arbitrary misrepresentation function whose running time is polynomial in the input size as long as the number of leaves of the underlying tree is bounded by a constant. On the other hand, we prove that our problem remains computationally hard on trees that have bounded degree, diameter, or pathwidth. Finally, we show how to modify Trick's [1989] algorithm to check whether an election is single-peaked on a tree whose number of leaves does not exceed a given parameter λ.