Supplementary Material to “ Label Selection on Graphs ”
نویسندگان
چکیده
Krause et al. [2008] has an indirect proof that F ′ is not submodular. They give an example that shows the greedy algorithm can do arbitrarily bad when maximizing F ′ under a cardinality constraint. If F ′ were submodular the greedy algorithm would give a (1 − 1/e) approximation for maximizing under a cardinality constraint. We give a direct proof that F ′ is not submodular for completeness. In our proof, we specifically show this holds even when W ′ is symmetric with ∞ along the diagonal (i.e. for the restricted case of W ′ given by our graph covering problem).
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