Solving Steiner Tree Problems in Graphs with Lagrangian Relaxation
نویسندگان
چکیده
This paper presents an algorithm to obtain near optimal solutions for the Steiner tree problem in graphs. It is based on a Lagrangian relaxation of a multi-commodity flow formulation of the problem. An extension of the subgradient algorithm, the volume algorithm, has been used to obtain lower bounds and to estimate primal solutions. It was possible to solve several difficult instances from the literature to proven optimality without branching. Computational results are reported for problems drawn from the SteinLib library.
منابع مشابه
A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs
Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned by the PCS tree. Accordingly, the Prize...
متن کاملEfficient Algorithms for Solving Hypergraphic Steiner Tree Relaxations in Quasi-Bipartite Instances
We consider the Steiner tree problem in quasi-bipartite graphs, where no two Steiner vertices are connected by an edge. For this class of instances, we present an efficient algorithm to exactly solve the so called directed component relaxation (DCR), a specific form of hypergraphic LP relaxation that was instrumental in the recent break-through result by Byrka et al. [2]. Our algorithm hinges o...
متن کاملApproximating Node-Weighted k-MST on Planar Graphs
We study the problem of finding a minimum weight connected subgraph spanning at least k vertices on planar, node-weighted graphs. We give a (4 + ε)-approximation algorithm for this problem. In the process, we use the recent LMP primal-dual 3-approximation for the node-weighted prize-collecting Steiner tree problem [4] and the Lagrangian relaxation [6]. In particular, we improve the procedure of...
متن کاملSolving Steiner Tree roblem in raphs to ptimality
Absac In this paper we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms and primal heuristics. We are able to solve all problem instances discussed in literature to optimality, including one to our knowledge not ...
متن کاملApproximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs
Abstract. We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a (2.88+ǫ)-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Optim.
دوره 7 شماره
صفحات -
تاریخ انتشار 2003