A polynomial algorithm for the min-cut linear arrangement of trees
Journal of the ACM (JACM)
Heuristics for backplane ordering
Advances in VLSI and Computer Systems
On minimizing width in linear layouts
Discrete Applied Mathematics
Optimal linear labelings and eigenvalues of graphs
Discrete Applied Mathematics
Cluster analysis for hypertext systems
SIGIR '93 Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval
SIAM Journal on Computing
A survey of graph layout problems
ACM Computing Surveys (CSUR)
A Polyhedral Approach to Planar Augmentation and Related Problems
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Experiments on the minimum linear arrangement problem
Journal of Experimental Algorithmics (JEA)
Polynomial time algorithms for the MIN CUT problem on degree restricted trees
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Decorous Lower Bounds for Minimum Linear Arrangement
INFORMS Journal on Computing
A probabilistic heuristic for a computationally difficult set covering problem
Operations Research Letters
Variable Formulation Search for the Cutwidth Minimization Problem
Applied Soft Computing
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The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solutions or a reduced relative gap (difference between upper and lower bounds) on the instances tested. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the small instances (up to 32 vertices) as well as some of the large instances tested (up to 158 vertices) using less than 30 minutes of CPU time. We compare the results of our method with previous lower bounds, and with the best previous linear integer formulation solved using Cplex. Both comparisons favor the proposed procedure.