Approximating Directed Weighted-Degree Constrained Networks

Given a graph H = (V, F) with edge weights {w(e) : e F}, the weighted degree of a node v in H is {w(vu) : vu F}. We give bicriteria approximation algorithms for problems that seek to find a minimum cost directed graph that satisfies both intersecting supermodular connectivity requirements and weighted degree constraints. The input to such problems is a directed graph G = (V, E), edge-costs {c(e) : e E}, edge-weights {w(e) : e E}, an intersecting supermodular set-function f on V , and degree bounds {b(v) : v V }. The goal is to find a minimum cost f-connected subgraph H = (V, F) (namely, at least f(S) edges in F enter every S V ) of G with weighted degrees b(v). Our algorithm computes a solution of cost 2

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Zeev Nutov
• Keywords: Algorithm, Algorithms, APPROX 2008, Directed Graph, Weighted Degree