TY - GEN
T1 - Fast approximation algorithms for the generalized survivable network design problem
AU - Feldmann, Andreas Emil
AU - Könemann, Jochen
AU - Pashkovich, Kanstantsin
AU - Sanità, Laura
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In a standard f-connectivity network design problem, we are given an undirected graph G = (V, E), a cut-requirement function f : 2V → N, and non-negative costs c(e) for all e ∈ E. We are then asked to find a minimum-cost vector x ∈ ℕE such that x(δ(S)) ≥ f(S) for all S ⊆ V. We focus on the class of such problems where f is a proper function. This encodes many well-studied NP-hard problems such as the generalized survivable network design problem. In this paper we present the first strongly polynomial time FPTAS for solving the LP relaxation of the standard IP formulation of the f-connectivity problem with general proper functions f. Implementing Jain's algorithm, this yields a strongly polynomial time (2 + ε)-approximation for the generalized survivable network design problem (where we consider rounding up of rationals an arithmetic operation).
AB - In a standard f-connectivity network design problem, we are given an undirected graph G = (V, E), a cut-requirement function f : 2V → N, and non-negative costs c(e) for all e ∈ E. We are then asked to find a minimum-cost vector x ∈ ℕE such that x(δ(S)) ≥ f(S) for all S ⊆ V. We focus on the class of such problems where f is a proper function. This encodes many well-studied NP-hard problems such as the generalized survivable network design problem. In this paper we present the first strongly polynomial time FPTAS for solving the LP relaxation of the standard IP formulation of the f-connectivity problem with general proper functions f. Implementing Jain's algorithm, this yields a strongly polynomial time (2 + ε)-approximation for the generalized survivable network design problem (where we consider rounding up of rationals an arithmetic operation).
KW - Generalized survivable network design
KW - Primal-dual method
KW - Strongly polynomial runtime
UR - http://www.scopus.com/inward/record.url?scp=85010723569&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2016.33
DO - 10.4230/LIPIcs.ISAAC.2016.33
M3 - Conference contribution
AN - SCOPUS:85010723569
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 33.1-33.12
BT - 27th International Symposium on Algorithms and Computation, ISAAC 2016
A2 - Hong, Seok-Hee
PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik
T2 - 27th International Symposium on Algorithms and Computation, ISAAC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -