Efficient algorithms for the minimum shortest path Steiner arborescence problem with applications to VLSI physical design

Abstract

Given an undirected graph G = V;E with positive e d g e w eights lengths w : E ! + , a set of terminals sinks N V , and a unique root node r 2 N, a shortest-path Steiner arborescence simply called an arborescence in the following is a Steiner tree rooted at r spanning all terminals in N such t h a t e v ery sourceto-sink path is a shortest path in G. G i v en a triple G; N; r, the Minimum Shortest-Path Steiner Arborescence MSPSA problem seeks an arborescence with minimum weight. The MSPSA problem has various applications in the areas of VLSI physical design, multicast network communication, and supercomputer message routing; various cases have been studied in the literature. In this paper, we propose several heuristics and exact algorithms for the MSPSA problem with applications to VLSI physical design. Experiments indicate that our heuristics generate near-optimal results and achieve speedups of orders of magnitude over existing algorithms.

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

“…Further applications include many practical integer programming problems. Shortest-paths computations are used as subroutines in solution procedures for computational biology (DNA sequence alignment [68]), VLSI design [8], knapsack packing problems [25], and traveling salesman problems [43] and for many other problems. A diverse set of shortest-paths models and algorithms have been developed to accommodate these various applications [11].…”

Gaining Predictability and Noise Immunity in Global Interconnects

“…This function is the same as function RSA/G(P, N, deleted) shown in Table 1 in [11] except that we compute the width for each segment. Note that when no nodes are deleted, this function becomes a heuristic algorithm for constructing an RSA tree.…”

“…Two cases are possible. We generalize the MRSA (Minimum Rectangular Steiner Arborescence) tree routing algorithm [11] to solve such a variable-width wire routing problem and develop a new router to implement bundled communication. The MRSA algorithm was chosen mainly because it constructs the routing structure from sinks to the source.…”

“…It has been shown that P together with C, the total wire length in all subtrees, and S, the set of selected Steiner points, can completely characterize the constructed partial arborescence tree. All formal definitions can be found in [11].…”

“…The MRSA algorithm [11] is based on branch-andbound. The nodes in the routing graph are ranked by their distances from the source terminal.…”