PTAS for Minimax Approval Voting
Abstract
We consider Approval Voting systems where each voter decides on a subset to candidates he/she approves. We focus on the optimization problem of finding the committee of fixed size k minimizing the maximal Hamming distance from a vote. In this paper we give a PTAS for this problem and hence resolve the open question raised by Carragianis et al. [AAAI'10]. The result is obtained by adapting the techniques developed by Li et al. [JACM'02] originally used for the less constrained Closest String problem. The technique relies on extracting information and structural properties of constant size subsets of votes.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.7216
- arXiv:
- arXiv:1407.7216
- Bibcode:
- 2014arXiv1407.7216B
- Keywords:
-
- Computer Science - Data Structures and Algorithms;
- Computer Science - Computational Complexity;
- Computer Science - Computer Science and Game Theory;
- 68W25;
- 68Q17;
- 05C12;
- 91B12 (Primary);
- 68Q87;
- 68W32;
- 90C05;
- 90C47 (Secondary);
- G.1.6;
- F.2.2
- E-Print:
- 15 pages, 1 figure