Journal of Computer and System Sciences
Invitation to data reduction and problem kernelization
ACM SIGACT News
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Determining possible and necessary winners under common voting rules given partial orders
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Incompleteness and incomparability in preference aggregation
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On problems without polynomial kernels
Journal of Computer and System Sciences
A multivariate complexity analysis of determining possible winners given incomplete votes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Taking the Final Step to a Full Dichotomy of the Possible Winner Problem in Pure Scoring Rules
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
The complexity of online manipulation of sequential elections
Journal of Computer and System Sciences
Annals of Mathematics and Artificial Intelligence
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The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes (partial orders) are extended into complete ones (linear orders) in a favorable way. Under the k-approval protocol, for every voter, the best k candidates of his or her preference order get one point. A candidate with maximum total number of points wins. The POSSIBLE WINNER problem for k-approval is NP-complete even if there are only two votes (and k is part of the input). In addition, it is NP-complete for every fixed k ∈ {2,...,m - 2} with m denoting the number of candidates if the number of votes is unbounded. We investigate the parameterized complexity with respect to the combined parameter k and "number of incomplete votes" t, and with respect to the combined parameter k′ := m - k and t. For both cases, we use kernelization to show fixed-parameter tractability. However, we show that whereas there is a polynomial-size problem kernel with respect to (t, k′), it is very unlikely that there is a polynomial-size kernel for (t, k). We provide additional fixed-parameter algorithms for some special cases.