# Committee selection with multimodal preferences

##### Citations

2 citations

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2,195 citations

### "Committee selection with multimodal..." refers background in this paper

...A particularly popular domain restriction is the single-peaked domain, originally proposed by Black [6]....

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659 citations

### "Committee selection with multimodal..." refers methods in this paper

...We provide a polynomial time reduction from the W[1]hard problem Independent Set (IS) [12]....

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...Towards this, we give a reduction from the W[1]-hard problem Independent Set (IS) [12], in which given a graph G and an integer t; we shall decide the existence of a t-sized set X ⊆ V (G) containing only nonadjacent vertices....

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220 citations

### "Committee selection with multimodal..." refers background in this paper

...Due to Proposition 4 and the fact that Egalitarian-CC is NP-hard and W[2]-hard w.r.t. the committee size k [5], we have following result....

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...In particular, while finding winning committees under kBorda can be done in polynomial time (one has to select k candidates with the highest individual Borda scores), CC is NP-hard [26] but FPTfor certain parameters, admit approximation algorithms, and certain heuristics are known to be effective for it [5, 20, 28, 15]....

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...Due to Proposition 3 and the fact that CC is NP-hard and W[2]-hard w.r.t. k [5], we obtain the following result....

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...Corollary 8 Min-CC, Sum-CC, and Vector-CC are NP-hard and W[2]-hard w.r.t. k even for Local-SP, and n = 1 We next study the computational complexity of Max-CC for Global-SP profiles, and obtain intractability....

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...Due to Proposition 2, and NP-hardness and W[2]-hardness of EgalitarianCC with respect to the committee size k [5], we obtain: Corollary 4 Min-CC is NP-hard and W[2]-hard w.r.t. k even for n = 1....

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215 citations

### "Committee selection with multimodal..." refers background or methods in this paper

...We adapt the corresponding algorithm for CC [5]: We guess a clustering of the voters (i....

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...Due to Proposition 2, and NP-hardness and W[2]-hardness of EgalitarianCC with respect to the committee size k [5], we obtain:...

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...[5] for Max-CC and Min-CC under Global-SP; unfortunately,...

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...In particular, a polynomial time algorithm, computing winning committees under CC for single-peaked profiles is known [5]....

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...k [5], we obtain the following result....

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214 citations

### "Committee selection with multimodal..." refers background in this paper

..., [16] and [17]), k-Borda and CC represent two extreme multiwinner rules....

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...As k-Borda is in P [17], we have the following:...

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...We obtain tractability in polynomial time; due to Proposition 1 and the fact that k-Borda can be solved in polynomial time [17], we have the following result....

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