VLSI layout applications yield instances of the Steiner tree problem over grid graphs with holes, which are considered hard to be solved by current methods. In particular, preprocessing techniques developed for Steiner problems over general graphs are not likely to reduce signiicantly such VLSI instances. We propose a new preprocessing procedure, combining earlier ideas from the literature to m...

In 2002, J. Díaz, M. Serna and the author published “A Survey of Graph Layout Problems”, which then was a complete view of the current state of the art of layout problems from an algorithmic point of view. The current review expands the contents of the original survey with updated results from these latest ten years and contributes an extensive bibliography.

Graph layout problems such as node and edge overlapping occur widely in many industrial computer-aided design applications. Usually, these problems are handled in an ad hoc manner by some specially designed algorithms. GENET and its extended model EGENET are local search methods used to solve constraint satisfaction problems such as the car-sequencing problems efficiently. Both models use the m...

In this paper, we study the approximability of several layout problems on a family of random geometric graphs. Vertices of random geometric graphs are randomly distributed on the unit square and are connected by edges whenever they are closer than some given parameter. The layout problems that we consider are: Bandwidth, Minimum Linear Arrangement, Minimum Cut Width, Minimum Sum Cut, Vertex Sep...

Spatial layout problems aaect architects, physicists and many other professionals in their attempts to streamline factory designs, nd optimal molecular con-gurations or arrange components for micro-circuitry design. Although genetic algorithms have been used successfully in many of these areas, certain aspects of these problems still represent a major challenge for the GA community. This paper ...

In the framework of parameterized complexity, one of the most commonly used structural parameters is the treewidth of the input graph. The reason for this is that most natural graph problems turn out to be fixed parameter tractable when parameterized by treewidth. However, Graph Layout problems are a notable exception. In particular, no fixed parameter tractable algorithms are known for the Cut...

We show that, with overwhelming probability, several well known layout problems are approximable within a constant for random graphs drawn from the G(n, pn) model where C/n ≤ pn ≤ 1 for all n big enough and for some properly characterized parameter C > 1. In fact, our results establish that, with overwhelming probability, the cost of any arbitrary layout of such a random graph is within a const...

The VLSI layout designing is a highly complex process and hence a layout is often subjected to Layout Verification that includes (a) Design Rule Checking to check if the layout satisfies various design rules and (b) Connectivity Extraction to check if the components of the layout are properly electrically connected. In this work we study two geometric query problems which have applications in t...

there are some problems with estimating the time required for the manufacturing process of products, especially when there is a variable serving time, like control stage. these problems will cause overestimation of process time. layout constraints, reworking constraints and inflexible product schedule in multi product lines need a precise planning to reduce volume in particular situation of lin...

A facility layout problem is concerned with determining the best position of departments, cells, or machines on the plant. An efficient layout contributes to the overall efficiency of operations. It’s been proved that, when system characteristics change, it can cause a significant increase in material handling cost. Consequently, the efficiency of the current layout decreases or is lost and it ...