Approximating Steiner trees in graphs with restricted weights
نویسندگان
چکیده
We analyze the approximation ratio of the average distance heuristic for the Steiner tree problem on graphs, and prove nearly tight bounds for the cases of complete graphs with binary weights f1; dg, or weights in the interval 1; d], where d 2. The improvement over other analyzed algorithms is a factor of about e 2:718.
منابع مشابه
Steiner Point Removal in Graph Metrics
Given a family of graphs F , and graph G ∈ F with weights on the edges, the vertices of G are partitioned into terminals T and Steiner nodes S. The shortest paths (according to edge weights) define a metric on the set of vertices. We wish to embed the set T in a weighted graph G′ ∈ F such that the distance between any two vertices x, y ∈ T in the graph G′ is “close” to their distance in G. More...
متن کاملApproximation Algorithms for Facility Location with Capacitated and Length-Bounded Tree Connections
We consider a generalization of the uncapacitated facility location problem that occurs in planning of optical access networks in telecommunications. Clients are connected to open facilities via depthbounded trees. The total demand of clients served by a tree must not exceed a given tree capacity. We investigate a framework for combining facility location algorithms with a tree-based clustering...
متن کاملA combinatorial approximation algorithm for the group Steiner problem
In the group Steiner problem we are given a graph with edge weights w(e) and m subsets of vertices fg i g m i=1. Each subset g i is called a group and the vertices in S g i are called terminals. It is required to nd a minimum weight tree that contains at least one terminal from every group. We present the rst combinatorial poly-logarithmic ratio approximation for this problem when the input gra...
متن کاملFinding a Noncrossing Steiner Forest in Plane Graphs Under a 2-Face Condition
Let G = (V, E) be a plane graph with nonnegative edge weights, and letN be a family of k vertex sets N1, N2, . . . , Nk ⊆ V , called nets. Then a noncrossing Steiner forest forN in G is a set T of k trees T1, T2, . . . , Tk in G such that each tree Ti ∈ T connects all vertices, called terminals, in net Ni , any two trees in T do not cross each other, and the sum of edge weights of all trees is ...
متن کاملApplications of the Linear Matroid Parity Algorithm to Approximating Steiner Trees
The Steiner tree problem in unweighted graphs requires to find a minimum size connected subgraph containing a given subset of nodes (terminals). In this paper we investigate applications of the linear matroid parity algorithm to the Steiner tree problem for two classes of graphs: where the terminals form a vertex cover and where terminals form a dominating set. As all these problems are MAX-SNP...
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:
- Networks
دوره 31 شماره
صفحات -
تاریخ انتشار 1998