TY - GEN
T1 - Near-Tight Algorithms for the Chamberlin-Courant and Thiele Voting Rules
AU - Sornat, Krzysztof
AU - Williams, Virginia Vassilevska
AU - Xu, Yinzhan
N1 - Publisher Copyright:
© 2022 International Joint Conferences on Artificial Intelligence. All rights reserved.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - We present an almost optimal algorithm for the classic Chamberlin-Courant multiwinner voting rule (CC) on single-peaked preference profiles. Given n voters and m candidates, it runs in almost linear time in the input size improving the previous best O(nm2) time algorithm. We also study multiwinner voting rules on nearly single-peaked preference profiles in terms of the candidate-deletion operation. We show a polynomial-time algorithm for CC where a given candidate-deletion set D has logarithmic size. Actually, our algorithm runs in 2|D|· poly(n, m) time and the base of the power cannot be improved under the Strong Exponential Time Hypothesis. We also adapt these results to all non-constant Thiele rules which generalize CC with approval ballots.
AB - We present an almost optimal algorithm for the classic Chamberlin-Courant multiwinner voting rule (CC) on single-peaked preference profiles. Given n voters and m candidates, it runs in almost linear time in the input size improving the previous best O(nm2) time algorithm. We also study multiwinner voting rules on nearly single-peaked preference profiles in terms of the candidate-deletion operation. We show a polynomial-time algorithm for CC where a given candidate-deletion set D has logarithmic size. Actually, our algorithm runs in 2|D|· poly(n, m) time and the base of the power cannot be improved under the Strong Exponential Time Hypothesis. We also adapt these results to all non-constant Thiele rules which generalize CC with approval ballots.
UR - http://www.scopus.com/inward/record.url?scp=85137876922&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85137876922
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 482
EP - 488
BT - Proceedings of the 31st International Joint Conference on Artificial Intelligence, IJCAI 2022
A2 - De Raedt, Luc
A2 - De Raedt, Luc
PB - International Joint Conferences on Artificial Intelligence
T2 - 31st International Joint Conference on Artificial Intelligence, IJCAI 2022
Y2 - 23 July 2022 through 29 July 2022
ER -