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Past exam of the computer science course of the University of Oxford

2023

Combinatorial optimisation

For a <set function> $f:2^V\to\mathbb R$, the four properties are:

* A <normalised set function> satisfies \b[$f(\varnothing)=0$].
* A <nonnegative function> satisfies \b[$f(S)\geq0$ for every $S\subseteq V$].
* A <monotone set function> satisfies \b[$f(A)\leq f(B)$ whenever $A\subseteq B\subseteq V$].
* A <symmetric set function> satisfies \b[$f(S)=f(V\setminus S)$ for every $S\subseteq V$].

Here <monotone set function> means nondecreasing under inclusion; it does not require strict increase.

Solution

Past exam of the computer science course of the University of Oxford / 2023 / Combinatorial optimisation / 1 / a / Solution

Past exam of the computer science course of the University of Oxford / 2023 / Combinatorial optimisation / 1 / a / Solution

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Past exam of the computer science course of the University of Oxford / 2023 / Combinatorial optimisation / 1 / a / Solution

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