Journal ArticleDOI
Single Row Routing
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TLDR
This paper discusses the relevance of single row routing in the context of the general routing problem and obtains an O((2k)!kn log k) algorithm to determine whether or not an instance involving n nodes can be laid out when only k tracks per street are available.Abstract:
The automated design of multilayer printed circuit boards is of great importance in the physical design of complex electronic systems. Wire routing is a crucial step in the design process. In this paper, the single row routing problem is considered. First, we discuss the relevance of single row routing in the context of the general routing problem. Then, we show that relaxing the restriction that backward moves are not allowed can result in smaller street congestions when there are at least four tracks in each street. Next, we obtain an O((2k)!kn log k) algorithm to determine whether or not an instance involving n nodes can be laid out (without backward moves) when only k tracks per street are available. With the additional restriction that wires are not permitted to cross streets, an efficient (O(n2)) algorithm is obtained. This restricted problem is shown to be related to a furnace assignment problem.read more
Citations
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Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Book
Embedding graphs in books: a layout problem with applications to VLSI design
TL;DR: In this paper, the authors studied the problem of embedding a graph in a book with its vertices in a line along the spine of the book and its edges on the pages in such a way that edges residing on the same page do not cross.
Proceedings ArticleDOI
On the pagenumber of planar graphs
Jonathan F. Buss,Peter W. Shor +1 more
TL;DR: The pa#enumber or book thickness of a graph is the minimum number of pages required to embed the graph in a book; i.e., if the vertices are arranged along the spine of a book, the pagenumber is the number ofpages required to draw the edges without crossings.
Journal ArticleDOI
Algorithms for the fixed linear crossing number problem
TL;DR: Experimental results indicate that a heuristic based on the neural network model yields near-optimal solutions and outperforms the other heuristics, and experiments show the exact algorithm to be feasible for graphs with up to 50 edges, in general, although the quality of the initial upper bound is more critical to runing time than graph size.
Journal ArticleDOI
Planar embedding: linear-time algorithms for vertex placement and edge orderings
TL;DR: In this article, the problem of finding a planar embedding of a biconnected planar graph is discussed, based on the planarity testing algorithm of A. Lemple, et al. (1966) and its implementation using PQ-trees.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Proceedings ArticleDOI
Wire routing by optimizing channel assignment within large apertures
TL;DR: The purpose of this paper is to introduce a new wire routing method for two layer printed circuit boards based on the newly developed channel assignment algorithm and requires many via holes.
Proceedings ArticleDOI
A solution to line routing problems on the continuous plane
TL;DR: A new line-routing algorithm based on the continuous plane, which is much faster than the conventional method and has given good results when applied to many line- routing problems such as mazes, printed circuit boards, substrates, and PERT diagrams.