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On Chen and Chen’s new tree inclusion algorithm. (English) Zbl 1187.68678
Summary: Very recently, Y. Chen and Y. Chen [Inf. Process. Lett. 98, No. 6, 253–262 (2006; Zbl 1178.05091)] gave a new algorithm for the tree inclusion problem, which requires $$O(|T|\times \min\{\text{depth}(P),|\text{leaves}(P)|\})$$ time and no extra space. In this note, we show that there are flaws in their time-complexity analysis by presenting two counterexamples. We also give an example to show that the worst-case time complexity of their algorithm is non-polynomial. Consequently, the asymptotically most efficient algorithm for the tree inclusion problem is the former algorithm in [W. Chen, J. Algorithms 26, No. 2, 370–385 (1998; Zbl 0894.68109)].

MSC:
 68W05 Nonnumerical algorithms 68R10 Graph theory (including graph drawing) in computer science
Keywords:
trees; tree inclusion; algorithms
Full Text:
References:
 [1] Chen, W., More efficient algorithm for ordered tree inclusion, Journal of algorithms, 26, 370-385, (1998) · Zbl 0894.68109 [2] Chen, Y.; Chen, Y., A new tree inclusion algorithm, Information processing letters, 98, 253-262, (2006) · Zbl 1178.05091 [3] Kilpeläinen, P.; Mannila, H., Ordered and unordered tree inclusion, SIAM journal on computing, 24, 340-356, (1995) · Zbl 0827.68050 [4] Knuth, D.E., The art of computer programming, vol. 1, (1969), Addison-Wesley Reading, MA · Zbl 0191.17903 [5] Mannila, H.; Raiha, K.-J., On query languages for the p-string data model, (), 469-482 [6] Matoušek, J.; Thomas, R., On the complexity of finding iso- and other morphisms for partial k-trees, Discrete mathematics, 108, 343-364, (1992) · Zbl 0764.68128
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