Selected article for: "edge node and Multicolored Subgraph problem"
Author: Marcus Ludwig; Louis-Félix Nothias; Kai Dührkop; Irina Koester; Markus Fleischauer; Martin A. Hoffmann; Daniel Petras; Fernando Vargas; Mustafa Morsy; Lihini Aluwihare; Pieter C. Dorrestein; Sebastian Böcker
Title: ZODIAC: database-independent molecular formula annotation using Gibbs sampling reveals unknown small molecules
  • Document date: 2019_11_16
    • ID: 03uonbrv_74
    Snippet: The Multicolored Subgraph problem is a generalization of the Multicolored Clique problem; to this end, Lemma 1 can also be inferred from the complexity of Multicolored Clique, which is W[1]hard 52 . Assuming zero node and unit edge weights, the above construction implies that for any > 0, there is no polynomial time algorithm that approximates the maximum assignment weight to within a factor better than O(n 1− ), unless P = NP 53 . Furthermore,.....
    Document: The Multicolored Subgraph problem is a generalization of the Multicolored Clique problem; to this end, Lemma 1 can also be inferred from the complexity of Multicolored Clique, which is W[1]hard 52 . Assuming zero node and unit edge weights, the above construction implies that for any > 0, there is no polynomial time algorithm that approximates the maximum assignment weight to within a factor better than O(n 1− ), unless P = NP 53 . Furthermore, nding an assignment of weight k cannot be done in time n o(k) , unless the exponential time hypothesis fails 54,55 . Finally, we noted above that we can encode an arbitrary edge set E E * using zero edge weight for all e / ∈ E, so:

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