TY - CONF
T1 - Approximation and Parameterized Complexity of Minimax Approval Voting
AU - Cygan, Marek
AU - Kowalik, Łukasz
AU - Socała, Arkadiusz
AU - Sornat, Krzysztof
N1 - Funding Information:
Acknowledgments. Marek Cygan would like to thank Daniel Lokshtanov for helpful conversations about existing algorithms for the Closest (Sub)String problem. The authors thank Piotr Skowron for helpful remarks concerning the introduction and they thank reviewers for their insightful comments on the paper. The work of M. Cygan is a part of the project TOTAL that has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 677651). Ł. Kowalik and A. Socała were supported by the National Science Centre, Poland, grant number 2013/09/B/ST6/03136. K. Sornat was supported by the National Science Centre, Poland, grant number 2015/17/N/ST6/03684.
Publisher Copyright:
Copyright © 2017, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2017
Y1 - 2017
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&z.ast; (2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails. This means that the O&z.ast;(d2d) algorithm of Misra et al. [AAMAS 2015] is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O&z.ast;((3/e)2), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs intimenO(1/e2·log(1/ϵ)) · poly (m), almost matching the running time of the fastest known PTAS for CLOSEST STRING due to Ma and Sun [SIAM J. Comp. 2009].
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&z.ast; (2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails. This means that the O&z.ast;(d2d) algorithm of Misra et al. [AAMAS 2015] is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O&z.ast;((3/e)2), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs intimenO(1/e2·log(1/ϵ)) · poly (m), almost matching the running time of the fastest known PTAS for CLOSEST STRING due to Ma and Sun [SIAM J. Comp. 2009].
UR - http://www.scopus.com/inward/record.url?scp=85030478589&partnerID=8YFLogxK
M3 - Paper
SP - 459
EP - 465
T2 - 31st AAAI Conference on Artificial Intelligence, AAAI 2017
Y2 - 4 February 2017 through 10 February 2017
ER -