Approximation Algorithms for Priority Steiner Tree Problems

In the Priority Steiner Tree (PST) problem, we are given an undirected graph \(G=(V,E)\) with a source \(s \in V\) and terminals \(T \subseteq V \setminus \{s\}\), where each terminal \(v T\) requires nonnegative priority P(v). The goal is to compute minimum weight tree containing edges of varying rates such that path from s v consists rate greater than or equal PST problem k priorities admits \(\min \{2 \ln |T| + 2, k\rho \}\)-approximation [Charikar et al., 2004], hard approximate ratio \(c \log n\) for some constant c [Chuzhoy 2008]. this paper, first strengthen analysis provided by 2004] \((2 2)\)-approximation show approximation \(\lceil _2 \rceil 1 \le 1.443 2\), then provide very simple, parallelizable algorithm which achieves same ratio. We consider more difficult node-weighted version |T|+2)\)-approximation using extensions spider decomposition [Klein & Ravi, 1995]. This result in graphs. Moreover, ratios all above algorithms tight.