... because the dis-tances in this extended graph are based on the so-lution of the LP. The properties of this algorithmare given by the following two theorems (proofs inAppendix A).Theorem 2. The ... (2) The first summand accounts for the edges en-tirely within the region, and the second one ac-counts for the edges in C(v, r) to the extent thatthey are within the radius. The definition of ... +ni=1li j= 1v∈Di ,j ui,vw(Di)subject topi ,j, v= ui,v∀i, j& lt;li, v ∈ Di ,j (1)pi ,j, v+ ui,v≥ 1 ∀i, j& lt;li, v ∈Sk> ;j Di,k(2)pi ,j, v≤ pi ,j, u+ de∀i, j& lt;li, e=(u,v) ∈ E (3)de≥...