dc.contributor.author Bommireddi, Venkata Abhinav dc.date.accessioned 2017-09-28 16:56:57 (GMT) dc.date.available 2017-09-28 16:56:57 (GMT) dc.date.issued 2017-09-28 dc.date.submitted 2017-09-27 dc.identifier.uri http://hdl.handle.net/10012/12501 dc.description.abstract We show that for any constants $\epsilon > 0$ and $p \ge 1$, given oracle access to an unknown function $f : \{0,1\}^n \to [0,1]$ it is possible to determine if the function is submodular or is $\epsilon$-far from every submodular function, in $\ell_p$ distance, with a \emph{constant} number of queries to the oracle. We refer to the process of determining if an unknown function has a property, or is far from every function having the property, as \emph{property testing}, and we refer to the algorithm that does that as a tester or a testing algorithm. en A function $f : \{0,1\}^n \to [0,1]$ is a \emph{$k$-junta} if there is a set $J \subseteq [n]$ of cardinality $|J| \le k$ such that the value of $f$ on any input $x$ is completely determined by the values $x_i$ for $i \in J$. For any constant $\epsilon > 0$ and a set of $k$-juntas $\mathcal{F}$, we give an algorithm which determines if an unknown function $f : \{0,1\}^n \to [0,1]$ is $\frac{\epsilon}{10^6}$-close to some function in $\mathcal{F}$ or is $\epsilon$-far from every function in $\mathcal{F}$, in $\ell_2$ distance, with a constant number of queries to the unknown function. This result, combined with a recent junta theorem of Feldman and \Vondrak (2016) in which they show every submodular function is $\epsilon$-close, in $\ell_2$ distance, to another submodular function which is a $\tilde{O}(\frac{1}{\epsilon^2})$-junta, yields the constant-query testing algorithm for submodular functions. We also give 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. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Property testing en dc.subject Submodular functions en dc.subject Juntas en dc.title Testing Submodularity en dc.type Master Thesis en dc.pending false uws-etd.degree.department David R. Cheriton School of Computer Science en uws-etd.degree.discipline Computer Science en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Blais, Eric uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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