Making a profit as a high-dimensional store owner?
I'm not sure why you would need to enumerate the cliques. You can encode the distance constraints explicitly in just a quadratic number of constraints.

\begin{align*}&amp; &amp;&amp;\max_{S \in \lbrace 0, 1 \rbrace^n} \sum_{i=1}^n p_i s_i \tag*{}\\
&amp;\text{subject to} &amp;&amp;\sum_{i=1}^n c_i s_i \leq B \\
&amp; &amp;&amp; s_i + s_j \leq 1 \hspace{1cm} \forall j &gt; i \geq 1 \text{ where } d(x_i, x_j) \leq D \end{align*}