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Consider a polyhedron $\mathcal{P}$ defined by a set of linear inequalities, i.e.,

$$\mathcal{P} = \left\{ x \in \{0,1\}^N \mid Ax\le b \right\}$$

Suppose $\mathcal{P}\neq \emptyset$. If I have a point in $\mathcal{P}$, how to find its $K$-nearest neighbor vertices in $\mathcal{P}$?

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