Sketching valuation functions

Motivated by the problem of querying and communicating bidders’ valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the non-negative real numbers. We say that f is an α-sketch of f if for every set S, the value f (S) lies between f(S)/α and f(S), and f can be specified by poly(n) bits. We show that for every subadditive function f there exists an α-sketch where α = n1/2 · O(polylog(n)). Furthermore, we provide an algorithm that finds these sketches with a polynomial number of demand queries. This is essentially the best we can hope for since:

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Ashwinkumar Badanidiyuru, Shahar Dobzinski, Hu Fu, Robert Kleinberg, Noam Nisan, Tim Roughgarden
• Keywords: Algorithms, Combinatorial Auctions, Polylog, Polynomial Number, SODA 2012