Fast Approximation Algorithms for the Generalized Survivable Network Design Problem
نویسندگان
چکیده
In a standard f -connectivity network design problem, we are given an undirected graph G = (V,E), a cut-requirement function f : 2 → N, and non-negative costs c(e) for all e ∈ E. We are then asked to find a minimum-cost vector x ∈ N 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 + )-approximation for the generalized survivable network design problem (where we consider rounding up of rationals an arithmetic operation). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.1.6 Optimization
منابع مشابه
A Fast Strategy to Find Solution for Survivable Multicommodity Network
This paper proposes an immediately efficient method, based on Benders Decomposition (BD), for solving the survivable capacitated network design problem. This problem involves selecting a set of arcs for building a survivable network at a minimum cost and within a satisfied flow. The system is subject to failure and capacity restriction. To solve this problem, the BD was initially proposed with ...
متن کاملApproximation for Steiner Network
We present the first polynornial-time approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, also called the survivable network design problem. If k is the maximum cut requirement of the problem, our solution comes within a factor of 2k of optimal...
متن کاملInteger programming models and branch-and-cut approaches to generalized {0,1,2}-survivable network design problems
In this article, we introduce the Generalized [Formula: see text]-Survivable Network Design Problem ([Formula: see text]-GSNDP) which has applications in the design of backbone networks. Different mixed integer linear programming formulations are derived by combining previous results obtained for the related [Formula: see text]-GSNDP and Generalized Network Design Problems. An extensive computa...
متن کاملSurvivable Network Design with Degree or Order
We present algorithmic and hardness results for network design problems with degree or order constraints. The first problem we consider is the Survivable Network Design problem with degree constraints on vertices. The objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds Bv on the vertices. This includes the well-stu...
متن کاملA Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem*
We present a factor 2 approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, which is also known as the survivable network design problem. Our algorithm first solves the linear relaxation of this problem, and then iteratively rounds off the soluti...
متن کامل