The notion of Steiner visibility graphs is introduced. Their applicability in connection with the construction of good quality suboptimal solutions to the Euclidean Steiner tree problem with obstacles is discussed. Polynomial algorithms generating Steiner visibility graphs are described.

Steiner’s Problem is the “Problem of shortest connectivity”, that means, given a 3nite set of points in a metric space (X; ), search for a network interconnecting these points with minimal length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices di5erent from the points which are to be connected. Such points are called Steiner points. If w...

The Steiner tree is the underlying model for multicast communication. This paper presents a novel ant colony algorithm guided by problem relaxation for unconstrained Steiner tree in static wireless ad hoc networks. The framework of the proposed algorithm is based on ant colony system (ACS). In the first step, the ants probabilistically construct the path from the source to the terminal nodes. T...

Given a metric space on n points, an α-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of the induced subtree is within an α factor of the optimal Steiner tree cost for X. An α-approximate differentially private algorithm for the Steiner tree problem takes...

This paper presents the computational analysis of the Steiner tree problem on the Server-Client model of computation. In particular, this work analyzes the time delays among server and clients for the parallel Steiner tree algorithm and examines some consequences of time delays on the execution time by considering constant and variable delays. The paper also calculates the expression for the op...

Steiner tree problems occupy a central place in both areas of approximation and on-line algorithms. Many variants have been studied from the point of view of competitive analysis, and for several of these variants tight bounds are known. However, in several cases, worst-case analysis is overly pessimistic, and fails to explain the relative performance of algorithms. We show how parameterized an...

We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72 + 8nm), under the assumption that the length of the minimum Steiner tree is at most m+ q. This problem has extensive applications in taxonomy and biology. The Steiner tree problem in hypercu...

Given a metric space on n points, an α-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of the induced subtree is within an α factor of the optimal Steiner tree cost for X . An α-approximate differentially private algorithm for the Steiner tree problem take...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. In this note we investigate various properties of minimum Steiner trees in normed planes, i.e., where the "unit disk" is an arbitrary compact convex centrally symmetric domain D having nonempty interior. We show that if the boundary of D is strictly convex and di...

We have been developing a secure and reliable distributed storage system, which uses a secret sharing scheme. In order to efficiently store data in the system, this paper introduces an optimal share transfer problem, and proves it to be, generally, NP-hard. It is also shown that the problem can be resolved into a Steiner tree problem. Finally, through computational experiments we perform the co...