We describe a novel approach for constructing a single spanning tree for data aggregation towards a sink node which we call as Universal Steiner Tree (UST). The tree is universal in the sense that it is static and independent of the number of data sources and fusioncosts at intermediate nodes. The tree construction is in polynomial time, and for low doubling dimension topologies it guarantees a...

In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and bounded number of terminals.

We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose two scenario-based Steiner cut formulations, study the strength of the proposed valid inequalities, a...

Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the number of additional points is minimized. We propose using Steiner minimal trees to approximate minimum Steiner point trees. It is shown that in arbitrary metric spaces this gives a performance differe...

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.

We present critical-sink routing tree (CSRT) constructions which exploit available critical-path information to yield high-performance routing trees. Our CS-Steiner and "global slack removal" algorithms together modify traditional Steiner tree constructions to optimize signal delay at identified critical sinks. We further propose an iterative Elmore routing tree (ERT) construction which optimiz...

In the classical (min-cost) Steiner tree problem, we are given an edge-weighted undirected graph and a set of terminal nodes. The goal is to compute a min-cost tree S which spans all terminals. In this paper we consider the min-power version of the problem (a.k.a. symmetric multicast), which is better suited for wireless applications. Here, the goal is to minimize the total power consumption of...

In the Steiner tree problem, we are given as input a connected n-vertex graph with edge weights in {1, 2, . . . ,W}, and a subset of k terminal vertices. Our task is to compute a minimum-weight tree that contains all the terminals. We give an algorithm for this problem with running time O(7.97 ·n · logW ) using O(n · lognW · log k) space. This is the first single-exponential time, polynomial-sp...

In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided.

In this paper we present an heuristic for finding a near-optimal Euclidean Steiner Tree for a given set of terminal points. This is defined as the shortest length geometric construction that unites all the terminals. Our algorithm dynamically partitions the point set into multiple, separately optimized subsets. The Steiner tree for these subsets is constructed by running a highly modified genet...