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Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas

2013
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2013 IEEE 54th Annual Symposium on Foundations of Computer Science
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We investigate the approximability of several classes of real-valued functions by functions of a small number of variables (juntas). Our main results are tight bounds on the number of variables required to approximate a function f : {0, 1} n → [0, 1] within 2-error over the uniform distribution: • If f is submodular, then it is -close to a function of O( 1 2 log 1 ) variables. This is an exponential improvement over previously known results [1]. We note that Ω( 1 2 ) variables are necessary

doi:10.1109/focs.2013.32
dblp:conf/focs/FeldmanV13
fatcat:wpq2nientjb2he6em6psgfwwz4