论文信息 - Optimal one-page tree embeddings in linear time

Optimal one-page tree embeddings in linear time

In the minimum linear arrangement problem one wishes to assign distinct integers to the vertices of a given graph so that the sum of the differences (in absolute value) across the edges of the graph is minimized. This problem is known to be NP-complete for the class of all graphs, but polynomial for trees algorithms of time complexity O(n2.2) and O(n1.6) were given by Shiloach [SIAM J. Comput. 8 (1979) 15-32] and Chung [Comput. Math. Appl. 10 (1984) 43-60], respectively. We present a linear-time algorithm for finding the optimal embedding (arrangement) in a restricted but important class of embeddings called one-page embeddings.

Robert Hochberg | Matthias F. Stallmann

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