An edge-based heuristic for Steiner routing

Abstract

A new approximation heuristic for finding a rectilinear Steiner tree of a set of nodes is presented. It starts with a rectilinear minimum spanning tree of the nodes and repeatedly connects a node to the nearest point on the rectangular layout of an edge, removing the longest edge of the loop thus formed. A simple implementation of the heuristic using conventional data structures is compared with previously existing algorithms. The performance (i.e., quality of the route produced) of our algorithm is as good as the hest reported algorithm, while the running time is an order of magnitude better than that of this hest algorithm. It is also shown that the asymptotic time complexity for the algorithm can he improved to O(n log n), where n is the number of points in the set.

EBOARST: An Efficient Edge-Based Obstacle-Avoiding Rectilinear Steiner Tree Construction Algorithm

“…Borah et al [2] proposed an edge-substitution heuristic, a simple yet effective approach for Steiner tree refinement (on an obstacle-free plane). Zhou [7] observed that the geometrical proximity information embedded in the spanning graph could be leveraged to simplify the heuristic.…”

Multicriteria Network Design Using Evolutionary Algorithm

“…An increase in interconnect resistance increases interconnect delays thus making a dominant factor in timing analysis of VLSI circuits. The VLSI circuit design aims at finding minimum cost spanning/Steiner tree given delay bound constraints on source-sink connections [5]. Analogously, there exists the problem of degree/diameter-constrained minimum cost networks [6].…”

Efficient Steiner tree construction based on spanning graphs

“…Their algorithm and implementation had a worst case running time of , even though an alternative implementation was also proposed. Since the backbone is no longer restricted to the minimal spanning-tree topology, its performance was reported to be similar to the iterated 1-Steiner algorithm [2]. A recent effort in this direction is a new heuristic by Mandoiu et al [11], which is based on a 3/2 approximation algorithm of the metric Steiner tree problem on quasi-bipartite graphs [12].…”

“…To achieve that goal, we select the edge-substitution approach of Borah et al [2] as the basis, and enhance it with the spanning graph of Zhou et al [17] and other improvements. The implemented algorithm runs in time and takes storage, without large hidden constant.…”