Approximation Algorithms for Node-Weighted Directed Steiner Problems

Gianlorenzo D'Angelo, Esmaeil Delfaraz

Abstract: Guha et al. [STOC, 1999] and Moss and Rabani [SIAM J. Comput., 2007] introduced two variants of the Steiner problem in undirected graphs in which the nodes are associated with two values, called costs and prizes. In the budgeted rooted node-weighted Steiner tree problem, we are given an undirected graph G with n nodes, a predefined node r, costs and prizes associated to the nodes of G, and a budget \(B\). The aim is to find a tree in G rooted at r such that the total cost of its nodes is at most \(B\) and the total prize is maximized. In the quota rooted node-weighted Steiner tree problem, we are given a quota \(Q\), instead of the budget, and we aim at minimizing the cost of a tree rooted at r whose overall prize is at least \(Q\).