TY - JOUR
T1 - Approximation and parameterized complexity of minimax approval voting
AU - Cygan, Marek
AU - Kowalik, Lukasz
AU - Socala, Arkadiusz
AU - Sornat, Krzysztof
N1 - Publisher Copyright:
© 2018 AI Access Foundation. All rights reserved.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes. We show Minimax Approval Voting admits no algorithm running in time O∗(2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails. This means that the O∗(d2d) algorithm of Misra, Nabeel and Singh is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O∗((3=ϵ)2d), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for Minimax Approval Voting, which runs in time nO(1=ϵ2.log(1=ϵ)) . poly(m), where n is a number of voters and m is a number of alternatives. It almost matches the running time of the fastest known PTAS for Closest String due to Ma and Sun.
AB - We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes. We show Minimax Approval Voting admits no algorithm running in time O∗(2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails. This means that the O∗(d2d) algorithm of Misra, Nabeel and Singh is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O∗((3=ϵ)2d), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for Minimax Approval Voting, which runs in time nO(1=ϵ2.log(1=ϵ)) . poly(m), where n is a number of voters and m is a number of alternatives. It almost matches the running time of the fastest known PTAS for Closest String due to Ma and Sun.
UR - http://www.scopus.com/inward/record.url?scp=85057024593&partnerID=8YFLogxK
U2 - 10.1613/jair.1.11253
DO - 10.1613/jair.1.11253
M3 - Article
AN - SCOPUS:85057024593
SN - 1076-9757
VL - 63
SP - 495
EP - 513
JO - Journal Of Artificial Intelligence Research
JF - Journal Of Artificial Intelligence Research
ER -