Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Automatic graph drawing and readability of diagrams
IEEE Transactions on Systems, Man and Cybernetics
Crossing Minimization in Linear Embeddings of Graphs
IEEE Transactions on Computers
Graphs with E edges have pagenumber E O
Journal of Algorithms
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
The book crossing number of a graph
Journal of Graph Theory
CNMGRAF—graphic presentation services for network management
SIGCOMM '85 Proceedings of the ninth symposium on Data communications
Sorting Using Networks of Queues and Stacks
Journal of the ACM (JACM)
Algorithms for the fixed linear crossing number problem
Discrete Applied Mathematics
Book Embeddings and Crossing Numbers
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Linear and Book Embeddings of Graphs
Proceedings of the VLSI Algorithms and Architectures, Aegean Worksho on Computing
Computational Aspects of VLSI
A neural-network algorithm for a graph layout problem
IEEE Transactions on Neural Networks
K-pages graph drawing with multivalued neural networks
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
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The worst-case performances of some heuristics for the fixed linear crossing number problem (FLCNP) are analyzed. FLCNP is similar to the 2-page book crossing number problem in which the vertices of a graph are optimally placed on a horizontal "node line" in the plane, each edge is drawn as an arc in one half-plane (page), and the objective is to minimize the number of edge crossings. In FLCNP, the order of the vertices along the node line is predetermined and fixed. FLCNP belongs to the class of NP-hard optimization problems Masuda et al., 1990. In this paper we show that for each of the heuristics described, there exist classes of n-vertex, m-edge graphs which force it to obtain a number of crossings which is a function of n or m when the optimal number is a small constant. This leaves open the problem of finding a heuristic with a constant error bound for the problem.