Subadditive set function: Difference between revisions

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## Let for each <math>i\in \{1,2,\ldots,m\}, a_i:\Omega\rightarrow \mathbb{R}_+</math> be linear set functions. Then <math>f(S)=\max_{i}\left(\sum_{x\in S}a_i(x)\right)</math>

# Functions based on [[set cover]]. Let <math>T_1,T_2,\ldots,T_m\subseteq \Omega</math> such that <math>\cup_{i=1}^m T_i=\Omega</math>. Then <math>f</math> is defined as follows

{{space|10}} <math>f(S)=\textrm{min }t</math> such that there exists sets <math>T_{i_1},T_{i_2},\dots,T_{i_t}</math> satisfying <math>S\subseteq \cup_{j=1}^t T_{i_j}</math>

== Properties ==