VLSI cell placement problem is known to be NP complete. A wide repertoire of heuristic algorithms exists in the literature for efficiently arranging the logic cells on a VLSI chip. The objective of this paper is to present a comprehensive survey of the various cell placement techniques, with emphasis on standard ce11and macro

this article, we will review important developments in 1990s and discuss some open problems which may induce important developments in this centrary

The "Steiner minimal tree" (SMT) of a point set P is the shortest network of "wires" which will suffice to "electrically" interconnect P . The "minimum spanning tree" (MST) is the shortest such network when only intersite line segments are permitted. The "Steiner ratio" ae(P ) of a point set P is the length of its SMT divided by the length of its MST. It is of interest to understand which point set (or point sets) in R d have minimal Steiner ratio. In this paper, we introduce a point set in R d which we call the "d-dimensional sausage." The 1 and 2-dimensional sausages have minimal Steiner ratios 1 and p 3=2 respectively. (The 2-sausage is the vertex set of an infinite strip of abutting equilateral triangles. The 3sausage is an infinite number of points evenly spaced along a certain helix.) We present extensive heuristic evidence to support the conjecture that the 3-sausage also has minimal Steiner ratio (ß 0:784190373377122). Also: We prove that the regular tetrahedron minimize...

Dynamic proxy tree-based data dissemination schemes

Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we first give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Secondly, we present a new general local search approach which is based on a list of full Steiner trees constructed in a preprocessing phase. This list defines a solution space on which three neighbourhood structures are proposed and evaluated. Computational results show that this new approach is very competitive from a cost-benefit point of view. Furthermore, it has the advantage of being easy to apply to the Steiner tree problem in other metric spaces and to obstacle avoiding variants.

We present a class of O(n log n) heuristics for the Steiner tree problem in the Euclidean plane. These heuristics identify a small number of subsets with few, geometrically close, terminals using minimum spanning trees and other well-known structures from computational geometry: Delaunay triangulations, Gabriel graphs, relative neighbourhood graphs, and higher-order Voronoi diagrams. Full Steiner trees of all these subsets are sorted according to some appropriately chosen measure of quality. A tree spanning all terminals is constructed using greedy concatenation. New heuristics are compared with each other and with heuristics from the literature by performing extensive computational experiments on both randomly generated and library problem instances. Keywords: heuristics, Steiner trees 1 Introduction Given a set Z of n terminals in the Euclidean plane, a shortest network which interconnects Z is called a Steiner minimum tree (SMT). An SMT may contain additional intersection points, ...

We present approximation algorithms for several NP-hard optimization problems arising in network design. Almost all of our algorithms run in polynomial time and output solutions with a worst-case performance guarantee on the quality of the output solution. A typical problem that we consider can be stated as follows: given an undirected graph and certain connectivity requirements, find a subgraph that satisfies these requirements and has minimum cost. In this thesis, we address many different connectivity requirements such as spanning trees, Steiner trees, generalized Steiner forests, and two-connected networks. The cost criteria that we consider range from the total cost of the edges in the network, the total cost of the nodes in the network, the maximum degree of any node in the network, the maximum cost of any edge in the network to some combination of these. We also address the maximum-leaf spanning tree problem and provide the first approximation algorithms for this problem. In t...

In this paper, we present two techniques to analyze greedy approximation with nonsubmodular functions restricted submodularity and shifted submodularity. As an application of the restricted submodularity, we present a worst-case analysis of a greedy algorithm for Network Steiner tree adapted from a heuristic originally proposed by Chang in 1972 for Euclidean Steiner tree. The performance ratio of Chang’s heuristic is a longstanding open problem due to the nonsubmodularity of its potential function. As an application of the shifted submodularity, we present a worst-case analysis of a greedy algorithm for Connected Dominating Set generalized from a greedy algorithm proposed by Ruan et al. Such generalized greedy algorithm is shown to have performance ratio at most (1 + ε)(1 + ln( ∆ − 1)), which matches the well-known lower bound (1−ε)ln ∆, where ∆ is the maximum vertex-degree of input graph and ε is any positive constant.

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Topological network design is the process of planning the layout of a network subject to constraints on topology. Applications include the design of transportation and communication networks where the construction costs typically are associated with the nodes and/or edges of the network. The Steiner tree problem is one of the fundamental topological network design problems. The problem is to interconnect (a subset of) the nodes such that there is a path between every pair of nodes while minimizing the total cost of selected edges. Originally, the Steiner tree problem was stated as a purely geometric problem: Given a set of points (terminals) in the plane, construct a tree interconnecting all terminals such that the total length of all line segments is minimized. In the Euclidean Steiner tree problem, the length of a line segment is the usual Euclidean (or L 2 ) distance between the endpoints of the segment. Correspondingly, in the rectilinear Steiner tree problem distances are measured...