This paper gives fixed-parameter approximation schemes, a lossy kernel, and an additive approximation for submodular multiwinner election on K_{d,d}-free profiles, and proves FPT for PAV parameterized by total score.
Computational aspects of multi-winner approval voting
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More Efforts Towards Fixed-Parameter Approximability of Multiwinner Rules
This paper gives fixed-parameter approximation schemes, a lossy kernel, and an additive approximation for submodular multiwinner election on K_{d,d}-free profiles, and proves FPT for PAV parameterized by total score.