A Supplementary Material: Proofs 390 A.1 Missing Proofs from Section 3

To establish Lemmas 3.1 and 3.3, we build on the work of ( We recall the following notation from the main body of the paper. Lemma 3.1 is based on the construction of certain geometric partitions of A high-level idea behind the proof is explained in Figure 1. We now provide formal proof. Now we will prove that f satisfies the required properties. First, we prove the approximation guarantee.