We present a new algorithm that solves the minimum Steiner tree problem on an undirected graph with n nodes, k terminals, and m edges with bounded integer weights in time Õ((2− ε)n + nm). Our algorithm beats the aesthetically appealing and seemingly inherent 2 bound of the current best algorithm for Steiner tree problem from Björklund, Husfeldt, Kaski, and Koivisto. Our algorithm is based on fa...

In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group) . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building b...

The rectilinear Steiner tree problem i s t o find a manimum-length set of horizontal and vertical line segments that interconnect a given set of points in $he plane. Here we study the thumbnail rectilinear S te iner tree problem, where the inpvt points are drawn f r o m a small integer grid. Specifically, we devise a full-set decomposition algorithm for computing opt ima l thumbnail rectalinear...

We investigate the cost allocation strategy associated with the problem of providing some network service from source to a number of users, via the Minimum Cost Steiner Tree Network that spans the source and all the receivers. The cost of such a Steiner tree network, is distributed among its receivers. The objective of this paper is to develop a reasonably fair and computationally efficient cos...

We formulate the problem of constructing broadcast trees for real-time traffic with delay constraints in networks with asymmetric link loads as a delay-constrained minimum spanning tree (DCMST) problem in directed networks. Then, we prove that this problem is NP-complete, and we propose an efficient heuristic to solve the problem based on Prim’s algorithm for the unconstrained minimum spanning ...

Given a connected, undirected distance graph with required classes of nodes and optional Steiner nodes, nd a shortest tree containing at least one node of each required class. This problem called Class Steiner Tree is NP-hard and therefore we are dependent on approximation. In this paper, we investigate various restrictions of the problem comparing their complexities with respect to approximabi...

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...

We describe a technique to improve Smith’s branch-and-bound algorithm for the Euclidean Steiner tree problem inRd . The algorithm relies on the enumeration and optimization of full Steiner topologies for corresponding subsets of regular points. We handle the case of two Steiner points colliding during the optimization process—that is when there is a small enough distance between them—to dynamic...

The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even finding feasible solutions is already NP-hard. What makes this problem special is that in order to reach...