Fig. 4

Demonstration of the running time of canspell. A The current bucket \(b_{j}\) in S’s traversal stores \(K^{c}_{j}=label_{I}(u_{h}){\cdot }K^{c}[c_{\ell }\ldots c_r]{\cdot }label_D(v_{o-h})\) (dotted red line). The triangles are the tries I and D. B Sliding \(w_{\ell }, w_r\) \(x=1\) position to the left, and then \(x=1\) position to the right (i.e., visiting the next two buckets in S). The new node \(v_{o-h}\) is different from that of A because of Lemma 3. We already traversed the blue path and can not traverse it again due to Lemma 3. C, D The remaining window sliding options visiting \(u_{h}\). After (D), we can only slide \(w_{\ell }, w_r\) to the right without breaking Lemma 3. Therefore, we visited \(u_{h}\) \(\sigma -1=3\) times, with \(\sigma\) being the trie’s degree