This paper addresses the competitiveness of online algorithmsfor two Steiner Tree problems. In the online setting, requests for k ter-minals appear sequentially, and the algorithm must maintain a feasible,incremental solution at all times. In the first problem, the underlyinggraph is directed and has bounded asymmetry, namely the maximumweight of antiparallel links in the gr...

The Steiner Tree Problem with Delays (STPD) is a variant of the well-known Steiner Tree Problem in which the delay on each path between a source node and a terminal node is limited by a given maximum value. We propose a Branch-and-Cut algorithm for solving this problem using a formulation based on lifted Miller-TuckerZemlin subtour elimination constraints. The effectiveness of the proposed algo...

It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given...

Given a graph G = (V; E) and a positive integer k, the Phylogenetic k-Root Problem asks for a (unrooted) tree T without degree-2 nodes such that its leaves are labeled by V and (u; v) 2 E if and only if dT (u; v) k. If the vertices in V are also allowed to be internal nodes in T , then we have the Steiner k-Root Problem. Moreover, if a particular subset S of V are required to be internal nodes ...

In the automated design of road networks an important sub-task is the solution of an instance of the Steiner tree problem, a well known N P-hard problem. In this paper we present the experimental evaluation of a heuristic for the Steiner tree problem used in the design of low volume forest road networks. To evaluate a heuristic it is necessary to compare to the optimum value or a good lower bou...

Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we ®rst give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Seco...

We consider the currently strongest Steiner tree approximation algorithm that has recently been published by Goemans, Olver, Rothvoß and Zenklusen (2012). It first solves a hypergraphic LP relaxation and then applies matroid theory to obtain an integral solution. The cost of the resulting Steiner tree is at most (1.39 + ε)-times the cost of an optimal Steiner tree where ε tends to zero as some ...

Since 1971, numerous parameterized algorithms for the Steiner tree problem have been published, first of which was introduced by Dreyfus and Wagner. However, up to today there is not a single parameterized algorithm for the two-stage stochastic Steiner tree problem. This problem is still practically important and deserves more attention. This document first presents an algorithm that has a wors...

Many multiple alignment methods implicitly or explicitly try to minimize the amount of biological change implied by an alignment. At the level of sequences, biological change is measured along a phylogenetic tree, a structure frequently being predicted only after the multiple alignment instead of together with it. The Generalized Tree Alignment problem addresses both questions simultaneously. I...

We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G = (V, E) and an integer k, decide whether there exists F ⊆ V , |F | ≤ k, such that G[V \ F ] is a forest and G[F ] is connected. We show that Connected ...