Testing Submodularity and Other Properties of Valuation Functions

Eric Blais, Abhinav Bommireddi, Marc Herbstritt
2017 Innovations in Theoretical Computer Science  
We show that for any constant > 0 and p ≥ 1, it is possible to distinguish functions f : {0, 1} n → [0, 1] that are submodular from those that are -far from every submodular function in p distance with a constant number of queries. More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al. ( 2007 ) to show that every property of real-valued functions that is well-approximated in 2 distance by a class of k-juntas for some k = O(1) can be tested in the p -testing
more » ... odel with a constant number of queries. This result, combined with a recent junta theorem of Feldman and Vondrák ( 2016 ), yields the constant-query testability of submodularity. It also yields constant-query testing algorithms for a variety of other natural properties of valuation functions, including fractionally additive (XOS) functions, OXS functions, unit demand functions, coverage functions, and self-bounding functions.
doi:10.4230/lipics.itcs.2017.33 dblp:conf/innovations/BlaisB17 fatcat:o7vrglavaff2rkad2uoo2l3bz4