A New Heuristic Algorithm for the Linear Arrangement Problem

A new algorithm for the linear arrangement problem is described. The goal is to produce linear arrangements of software model diagrams such that the total length of all connections is reduced as much as possible. The algorithm uses the same general numbering strategy as existing algorithms for the highly related problems of bandwidth and profile reduction but is based on a new heuristic that addresses the unique requirements of the linear arrangement problem. Extensive testing is performed with graphs derived from software model diagrams and from structural engineering. The testing indicates that three refinements to the new algorithm improve the arrangements produced. The new algorithm produces linear arrangements with lower total weighted edge length for both classes of test graphs in comparison with several bandwidth and profile reduction algorithms, and for the software model diagrams in comparison with an eigenvalue-based linear arrangement algorithm. The new heuristic is also shown to require slightly less execution time than the frontal increase minimization heuristic used by several bandwidth and profile reduction algorithms, and far less execution time than the eigenvalue-based algorithm.