Abstract We have studied the Steiner tree problem using six-pin soap films in detail. We extend the existing method of experimental realisation of Steiner trees in n-terminal problem through soap films to observe new non-minimal Steiner trees. We also produced spanning tree configurations for the first time by our method. Experimentally, by varying the pin diameter, we have achieved these new s...

When relating a set of sequences by a phylogeny, we are essentially constructing a Steiner tree connecting the sequences in the space of all finite sequences. Finding an optimal Steiner tree is in most formulations hard, so population genetics and phylogenetics have often used spanning trees as an approximation for computational expediency. In this assessment you will be asked to investigate an...

In this work we present a branch-and-bound (B&B) framework for the asymmetric prizecollecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS) and the nodeweighted Steiner tree problem (NWSTP). The ma...

The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a two-phase scheme: First a small but suucient set of full Steiner trees (FSTs) is generated and then a Steiner minimum tree is constructed from this set by using simple backtrack search, dynamic programming or an integer programming formulation. FST generation methods can be seen as problem red...

We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane, called terminals, find a Steiner tree with at most k Steiner points such that the length of the longest edge in the tree is minimized. This problem is known to be NP-hard even to approximate within ratio √ 2. We focus on finding exact solutions to the problem for a small constant k. Based o...

The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem,...

Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given two vertices u, v in G, a short...

The terminal Steiner tree problem (TST) consists of finding a minimum cost Steiner tree where each terminal is a leaf. We describe a factor 2ρ−ρ/(3ρ−2) approximation algorithm for the TST, where ρ is the approximation factor of a given algorithm for the Steiner tree problem. Considering the current best value of ρ, this improves a previous 3.10 factor to 2.52. For the TST restricted to instance...

In this paper, we discuss the problem of reoptimization of Steiner tree. We are given an instance of Graph and also an optimal Steiner tree of it. If some changes occurs later on in the given graph. New optimal Steiner tree is to be determine, this process is known as re optimization. We consider two cases of change: one is addition of a new edge and second is, Deletion of an existing edge. For...

In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V , and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an r-t path for every terminal t ∈ X. The only known polylogarithmic approximations for Directed Steiner Tree run in quasi-polynomial time and the best polynomial time approximations only ac...