Four pages are necessary and sufficient for planar graphs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Linear and book embeddings of graphs
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
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
Bounds for the crossing number of the N-cube
Journal of Graph Theory
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
A new variation on hypercubes with smaller diameter
Information Processing Letters
Graphs with E edges have pagenumber E O
Journal of Algorithms
On VLSI layouts of the star graph and related networks
Integration, the VLSI Journal
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
Parallel and distributed computing handbook
Parallel and distributed computing handbook
The book crossing number of a graph
Journal of Graph Theory
Embedding de Bruijn, Kautz and shuffle-exchange networks in books
Discrete Applied Mathematics
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
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)
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Properties and Performance of Folded Hypercubes
IEEE Transactions on Parallel and Distributed Systems
The Crossed Cube Architecture for Parallel Computation
IEEE Transactions on Parallel and Distributed Systems
A Theoretical Network Model and the Hamming Cube Networks
Proceedings of the 8th International Symposium on Parallel Processing
Book Embeddings and Crossing Numbers
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Computational Aspects of VLSI
A neural-network algorithm for a graph layout problem
IEEE Transactions on Neural Networks
An analysis of some linear graph layout heuristics
Journal of Heuristics
Genetic algorithms for the 2-page book drawing problem of graphs
Journal of Heuristics
Parallelisation of genetic algorithms for the 2-page crossing number problem
Journal of Parallel and Distributed Computing
Approximating the fixed linear crossing number
Discrete Applied Mathematics
Two pages graph layout via recurrent multivalued neural networks
IWANN'07 Proceedings of the 9th international work conference on Artificial neural networks
K-pages graph drawing with multivalued neural networks
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Fixed linear crossing minimization by reduction to the maximum cut problem
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Planar crossing numbers of genus g graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
| Hi-index | 0.04 |
several heuristics and an exact branch-and-bound algorithm are described for the fixed linear crossing number problem (FLCNP). An experimental study comparing the heuristics on a large set of test graphs is given. 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 this restricted version of the problem, the order of the vertices along the node line is predetermined and fixed. FLCNP belongs to the class of NP-hard optimization problems (IEEE Trans. Comput. 39 (1) (1990) 124). The heuristics are tested and compared on a variety of graphs including some "real world" instances of interconnection networks proposed as models for parallel computing. The experimental results indicate that a heuristic based on the neural network model yields near-optimal solutions and outperforms the other heuristics. Also, 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.