Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Simulated annealing: theory and applications
Simulated annealing: theory and applications
Local optimization and the traveling salesman problem
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Ordering problems approximated: single-processor scheduling and interval graph completion
Proceedings of the 18th international colloquium on Automata, languages and programming
Optimal linear labelings and eigenvalues of graphs
Discrete Applied Mathematics
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Generating lower bounds for the linear arrangement problem
Discrete Applied Mathematics
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SIAM Journal on Computing
Path optimization for graph partitioning problems
Discrete Applied Mathematics - Special volume on VLSI
Finding near-optimal cuts: an empirical evaluation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximating layout problems on random geometric graphs
Journal of Algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Linear Layouts of Generalized Hypercubes
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
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FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Topics in black-box combinatorial optimization
Topics in black-box combinatorial optimization
Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs
Combinatorics, Probability and Computing
Graph minimum linear arrangement by multilevel weighted edge contractions
Journal of Algorithms
A Genetic Hillclimbing Algorithm for the Optimal Linear Arrangement Problem
Fundamenta Informaticae
An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem
Computers and Operations Research
Multilevel algorithms for linear ordering problems
Journal of Experimental Algorithmics (JEA)
Parameterized algorithmics for linear arrangement problems
Discrete Applied Mathematics
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Proceedings of the third ACM conference on Recommender systems
Decorous Lower Bounds for Minimum Linear Arrangement
INFORMS Journal on Computing
Branch and bound for the cutwidth minimization problem
Computers and Operations Research
A Genetic Hillclimbing Algorithm for the Optimal Linear Arrangement Problem
Fundamenta Informaticae
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International Journal of Swarm Intelligence Research
Variable Formulation Search for the Cutwidth Minimization Problem
Applied Soft Computing
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Information Sciences: an International Journal
Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures
Proceedings of the 50th Annual Design Automation Conference
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This paper deals with the Minimum Linear Arrangement problem from an experimental point of view. Using a testsuite of sparse graphs, we experimentally compare several algorithms to obtain upper and lower bounds for this problem. The algorithms considered include Successive Augmentation heuristics, Local Search heuristics and Spectral Sequencing. The testsuite is based on two random models and "real life" graphs. As a consequence of this study, two main conclusions can be drawn: On one hand, the best approximations are usually obtained using Simulated Annealing, which involves a large amount of computation time. Solutions found with Spectral Sequencing are close to the ones found with Simulated Annealing and can be obtained in significantly less time. On the other hand, we notice that there exists a big gap between the best obtained upper bounds and the best obtained lower bounds. These two facts together show that, in practice, finding lower and upper bounds for the Minimum Linear Arrangement problem is hard.