# Dictionary Encoding Based on Tagged Sentential Decision Diagrams
## 5 Experimental Results
For each dictionary, the node count of the decision diagram with the minimum node count among all decision diagrams for each encoding method is highlighted in bold so that readers can intuitively see which decision diagram performs the best in node count. We first consider the decision diagrams that are encoded with the compact code in a one-hot way. Taking the dictionary _phpbb_ as an example, we can see that the ZDD and CZDD have the same and minimum node counts, while the CBDD has the second-smallest node count among all decision diagrams. The node count of the CBDD is 344,800, which is just 332 more than that of the BDD and CZDD. The node count of the ZSDD is larger than that of the ZDD, CZDD, and CBDD, and hence, it has the third-smallest node count. The node count of the TSDD is larger than that of the above decision diagrams. However, the node count still does not exceed 1.5 times the minimum value (the node count of ZDD or CZDD), that is, 446,421/344,468 = \(1.29<1.5\). The node counts of the SDD and BDD are much larger than those of the other decision diagrams, and the node count of the SDD is slightly smaller than that of the BDD. Hence, we can conclude that for the _node count_, among all the decision diagrams, the ZDD and CZDD have the best performance, and the performance of the CBDD, ZSDD, and TSDD is slightly inferior to that of the ZDD and CZDD, while the SDD and BDD perform the worst among all decision diagrams. For the encoding time, the performance of these decision diagrams is similar to that for the node count. We believe that the ZDD and CZDD take the minimum time to encode the dictionary. TSDDs perform worse than ZDDs and CZDDs in encoding time, while they are better than BDDs and SDDs. Although the performance of TSDDs is not very good when we encode in a one-hot way, it is not much worse than the best decision diagrams (ZDDs and CZDDs), and we can tolerate this drawback. For the other 13 dictionaries, the performance of these decision diagrams for node count and time is similar to that for _phpbb_. We believe that the Boolean function that represents the dictionary in a one-hot way is a spare Boolean function, which makes the performance of ZDDs, CZDDs, CBDDs, ZSDDs, and TSDDs better than that of SDDs and BDDs. The decision diagrams that are encoded by the ASCII code in a one-hot way include more variables than those that are encoded by the compact code in a one-hot way. Because they are both encoded in a one-hot way, they have similar performance for the node count and encoding time. For the decision diagrams that are encoded in a binary way, we focus on the performance of TSDDs. We can easily find that TSDDs have the minimum node count among all decision diagrams if we encode the same dictionary in a binary way, regardless of whether we use the compact code or ASCII code. Moreover, the node count of TSDDs may even be much smaller than that of other decision diagrams. For example, the node count of the TSDD that represents _dutch-wordlist_ with the ASCII code in a binary way is 273,022, while the second-smallest node count is 976,921, which is more than 3 times larger than that of