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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
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[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
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