On Maximum Symmetric Subgraphs
Chen, Ho-Lin and Lu, Hsueh-I. and Yen, Hsu-Chun (2001) On Maximum Symmetric Subgraphs. In: Graph Drawing 8th International Symposium, GD 2000, September 20–23, 2000, Colonial Williamsburg, VA, USA , pp. 372-383 (Official URL: http://dx.doi.org/10.1007/3-540-44541-2_35).
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Let G be an n-node graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NP-complete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability for the special cases of G being a plane graph, an ordered tree, and an unordered tree, depends on the type of operations used to obtain H from G. Moreover, we give an $O(\log n)$-approximation algorithm for the intractable case that H is obtained from a tree G by contracting edges. As a by-product, we give an $O(\log n)$-approximation algorithm for an NP-complete edit-distance problem.
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