More Approximation Algorithms Based on Linear Programming

In the context of this problem, we need to be very specific on choosing an uncovered sk, tk-path at each iteration. Fix a vertex r of G as the root of the tree. For each pair (si, ti), let LCA(si, ti) denote the least common ancestor of si and ti, which is the vertex at the intersection of the paths from si to r and from ti to r. Note that LCA(si, ti) could be si or ti. Let d(si, ti) denote the depth of LCA(si, ti), which is the distance between r and LCA(si, ti). Our primal-dual based algorithm is as follows. PRIMAL-DUAL FOR MULTICUT IN TREES 1: C ← ∅, y ← 0, j ← 0 2: while C is not a multicut do 3: Choose an uncovered path Pk with largest d(sk, tk)