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• 06:53, 28 November 2022 Roundgod talk contribs created page 高级算法 (Fall 2022)/Problem Set 3 (Created page with "== Problem 1 == Let <math>N</math> be a set (the "universe") and <math>F</math> a function mapping subsets of <math>N</math> to real numbers. There are two different standard definitions of what it means for <math>F</math> to be '''submodular''': (i) For all <math>A</math>, <math>B</math>, :<math>F(A\cap B)+F(A\cup B)\leq F(A)+F(B)</math>. (ii) For all <math>A\subseteq B</math>, <math>j\notin B</math>, :<math>F(A\cup\{j\})-F(A)\geq F(B\cup\{j\})-F(B)</math>. Your ta...")