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...

have also given a linear time algorithm to determine the set of possible root locations for a minimum diameter shortest path tree, and shown that any minimum diameter tree must pass through this region. When compared with the 1-Steiner algorithm, minimum diameter A-trees produced lower maximum and average delays, with slightly higher tree length. Consideration of the feasible center region resu...

We consider the Steiner k-cut problem which generalizes both the k-cut problem and the multiway cut problem. The Steiner k-cut problem is defined as follows. Given an edge-weighted undirected graph G = (V,E), a subset of vertices X ⊆ V called terminals, and an integer k ≤ |X|, the objective is to find a minimum weight set of edges whose removal results in k disconnected components, each of whic...

Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)-time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set of minimal Steiner trees and exploiting them in a dynamic programming algorithm.

Given a directed graph G = (V,E) and an integer k ≥ 1, a Steiner k-transitive-closure-spanner (Steiner k-TC-spanner) of G is a directed graph H = (VH , EH) such that (1) V ⊆ VH and (2) for all vertices v, u ∈ V , the distance from v to u in H is at most k if u is reachable from v in G, and ∞ otherwise. Motivated by applications to property reconstruction and access control hierarchies, we conce...

Two new approximate algorithms with O ( k l o g k ) for the rectilenear Steiner tree are proposed. Both algorithms base upon the method which makes minimum spanning tree on the modified Delaunay net with the triangular Steiner points as the more virtual generating points, because each point and each edge weight on the modified Delaunay net have been fixed.

the harary index h can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. a generalization of the harary index, denoted by hk, is achieved by employing the steiner-type distance between k-tuples of atoms. we show that the linear c...

Bottleneck Steiner tree problem asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. The problem has applications in the design of wireless communication networks. In this paper we study a restricted version of the bottleneck Steiner tree problem in the Euclidean plane which requires that only degree-2 Stein...

For a real number p ≥ 2, an integer k > 0 and a set of terminals X in the plane, the Euclidean power-p Steiner tree problem asks for a tree interconnecting X and at most k Steiner points such that the sum of the p-th powers of the edge lengths is minimised. We show that this problem is in the complexity subclass exp-APX (but not poly-APX) of NPO. We then demonstrate that the approximation algor...