# Dictionary Encoding Based on Tagged Sentential Decision Diagrams
## 5 Experimental Results
To reduce the node count of decision diagrams, we designed minimization algorithms for ZSDDs and TSDDs and applied them once to SDDs, ZSDDs, and TSDDs when over half of the words in the dictionary were encoded. The results of this experiment are shown in Table 2. Columns 1-2 report the names of the dictionaries and the word counts of the dictionaries. The names of the decision diagrams that represent the dictionaries are reported in column 3. Then, columns 4-11 report the node counts of decision diagrams and the encoding times using the four encoding methods. In our experiment, each dictionary contained over 100,000 words. In addition, we use '-' in place of data if the encoding time exceeded one hour. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dictionary**} & \multirow{2}{*}{**Word**} & \multirow{2}{*}{**Decision**} & \multirow{2}{*}{**Compact, One-Hot**} & \multirow{2}{*}{**Compact, Binary**} & \multirow{2}{*}{**ASCII, One-Hot**} & \multirow{2}{*}{**ASCII, Binary**} \\  & & & & & & & & & \\  & & \begin{tabular}{c} **Node** \\ **Count** \\ \end{tabular}  & \begin{tabular}{c} **Time/s** \\ **Count** \\ \end{tabular}  & \begin{tabular}{c} **Node** \\ **Count** \\ \end{tabular}  & \begin{tabular}{c} **Time/s** \\ **Count** \\ \end{tabular}  & \begin{tabular}{c} **Node** \\ **Time/s** \\ **Count** \\ \end{tabular}  & \begin{tabular}{c} **Time/s** \\ **Count** \\ \end{tabular}  \\ \hline \multirow{8}{*}{words} & \multirow{8}{*}{235,886} & BDD & 9,701,439 & 770.114 & 1,117,454 & 102.74 & 23,161,501 & 2583.639 & 1,464,773 & 116.729 \\  & & ZDD & **297.681** & 48.78 & 723,542 & 13.11 & **297.681** & 173.56 & 851,580 & 14.4 \\  & & CBDD & 626,070 & 97.671 & 1,007,868 & 69.721 & 626,071 & 96.365 & 1,277,640 & 117.756 \\  & & CZDD & **297.681** & 15.04 & 723,542 & 9.7 & **297.681** & 21.84 & 851,580 & 10.2 \\  & & SDD & 9,560,113 & 745.614 & 300,235 & 235.774 & 23,106,545 & 2011.952 & 536,433 & 260.563 \\  & & ZSDD & 298,995 & 221.506 & 443,883 & 224.212 & 305,232 & 225.827 & 740.462 & 248.588 \\  & & TSDD & 358,778 & 233.301 & **215.588** & 109.899 & 360,797 & 228.642 & **219.762** & 209.041 \\ \hline \multirow{8}{*}{password} & \multirow{8}{*}{979,247} & BDD & 49,231,085 & 3513.906 & 4,422,292 & 1061.895 & 790,914,931 & 3582.56 & 4,943,940 & 963.165 \\  & & ZDD & **1,130.729** & 713.15 & 2,506,088 & 52.52 & **1,130.729** & 658.21 & 2,875,612 & 50.77 \\  & & CBDD & 2,321,572 & 1734.869 & 3,597,474 & 710.504 & 2,321,792 & 1466.674 & 4,307,614 & 1466.614 \\  & & CZDD & **1,130.729** & 46.73 & 2,506,088 & 30.62 & **1,130.729** & 57.81 & 2,875,612 & 30.33 \\  & & SDD & - & - & 3,648,973 & 1074.062 & - & - & 3,979,717 & 1348.212 \\  & & ZSDD & 1,146,448 & 432.112 & 1,744,536 & 562.329 & 1,188,576 & 440.762 & 2,866,480 & 919.113 \\  & & TSDD & 1,356,869 & 1316.681 & **1,101.669** & 510.276 & 1,366,130 & 927.079 & **2,426.472** & 792.076 \\ \hline \multirow{8}{*}{\ \begin{tabular}{c} Ashley- \\ Madison \\ \end{tabular}  } & BDD & – & – & 2,111,727 & 364.746 & – & – & 2,082,848 & 280.353 \\  & & ZDD & **548.365** & 103.033 & 922,478 & 154.342 & **547.753** & 112.371 & 1,326,746 & 220.22 \\  & & CBDD & 548,724 & 498.307 & 1,033,895 & 199.4 & 695,493 & 427.79 & 1435,588 & 3301.287 \\  & & CZDD & **548.365** & 83.179 & 922,475 & 131.328 & **547.753** & 102.695 & 1,326,745 & 200.374 \\  & & SDD & - & - & 1,671,665 & 525.145 & – & - & 1,656,556 & 518.945 \\  & & ZSDD & 560,898 & 273.59 & 923,129 & 273.59 & 564,650 & 297.303 & 1,280,338 & 423.104 \\  & & TSDD & 596,396 & 351.467 & **420.810** & 228.901 & 595,493 & 369.138 & **965.362** & 333.126 \\ \hline \multirow{8}{*}{ \begin{tabular}{c} cain-and \\ -abel \\ \end{tabular}