The Steiner tree problem on weighted graphs seeks a minimum weight subtree containing a given subset of the vertices (terminals). We show that it is NP-hard to approximate the Steiner tree problem within a factor 96/95. Our inapproximability results are stated in a parametric way, and explicit hardness factors would be improved automatically providing gadgets and/or expanders with better parame...

Minimum Steiner tree problem in a weighted graph is to find a least cost sub tree in the graph such that it contains special vertices called terminal points. Since this problem belongs to NP-Complete problems, many approximate algorithms including genetic algorithms and ant colony strategies have been designed for solving it. In this paper, we propose an algorithm based on distributed learning ...

The network and Euclidean Steiner tree problems require a shortest tree spanning a given vertex subset within a network G = (V; E; d) and Euclidean plane, respectively. For these problems, we present a series of heuristics nding approximate Steiner tree with performance guarantee coming arbitrary close to 1+ln2 1:693 and 1+ln 2 p 3 1:1438, respectively. The best previously known corresponding v...

This paper presents an e cient algorithm for bu ered Steiner tree construction with wire sizing. Given a source and n sinks of a signal net, with given positions and a required arrival time associated with each sink, the algorithm nds a Steiner tree with bu er insertion and wire sizing so that the required arrival time (or timing slack) at the source is maximized. The unique contribution of our...

The minimum-energy multicast tree problem aims to construct a multicast tree rooted at the source node and spanning all the destination nodes such that the sum of transmission power at non-leaf nodes is minimized. However, aggressive power assignment at non-leaf nodes, although conserving more energy, results in multicast trees which suffer from higher hop count and jeopardizes delay-sensitive ...

The generalized steiner tree problem (GSTP) is a variant of the classical Steiner tree problem (STP), in which a family of node clusters is given and the tree must span at one node for each cluster. This note introduces a lifting procedure for obtaining polyhedral information on GSTP from polyhedral results of STP. New classes of facet-de ning inequalities are presented. ? 2000 Elsevier Science...

We study two-stage robust variants of combinatorial optimization problems like Steiner tree, Steiner forest, and uncapacitated facility location. The robust optimization problems, previously studied by Dhamdhere et al. [9], Golovin et al. [15], and Feige et al. [13], are two-stage planning problems in which the requirements are revealed after some decisions are taken in stage one. One has to th...

The total Steiner k-distance and the k-th total path length are the sum of the size of Steiner trees and ancestor-trees over sets of k nodes of a given tree, respectively. They are useful statistics with many applications. Consequently, they have been analyzed for many different random trees, including increasing tree, binary search tree, generalized m-ary search tree and simply generated trees...

Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of nding a shortest intercon-nection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well-known rectilinear Steiner tree problem which has direct applications in VLSI design, i.e., it is the fundamental prob...