# Analytics on Anonymity for Privacy Retention in Smart Health Data +
## 4 Evaluation and Experiments
### On Correctness  
Consider Table 1 and the anonymity requirement \(R\) is \(<\) [Zip, Age, AC], 3 \(>\). Partial search tree obtained by Method 1 is shown in Figure 4.  
As shown in Figure 4, \(T\) corresponds to Table 1 and \(T_{2}\) is the table obtained from generalizing \(T\) on attribute Zip (or Table 4). Method 1 generates all possible generalized tables and choose a table with maximum number of rows among those with zero violation as a solution. The resulting table is shown in Table 5 = \(T_{5}\) (0, 21) (see Figure 4), which is the same result obtained by our approach. All violations are eliminated (since Rows 4 and 14, Rows 6 and 10, and Rows 11 and 13 has 3, 5, and 4 records, satisfying \(R\), respectively). Furthermore, \(T_{5}\) has 21 distinct rows as Rows 1 and 9 are merged. Method 1 (Exhaustive search) and our approach produce the same anonymized table. However, as we will see later that both computational costs are significantly different. A compromising approach between the two is to use a greedy search. By using the number of rows that violate the anonymity requirement as a heuristic and each time expand on the table with minimum violations (as it has the highest chance  
Figure 4: Search Tree obtained from Method 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Row** & **Sex** & **Alcohol Cons. ** & **Age** & **Zip** & **Weight** & **Race** & **Genetic Risk** & **\#Rec. ** \\ \hline
1,9 & F & Med & [35; 36; 37; 38; 39; 40; 41; 42; 43; 44] & 5200 \(*\) & 143 & Black & No & 1 + 2 \\
2 & F & Low & [35; 36; 37; 38; 39; 40; 41; 42; 43; 44] & 5200 \(*\) & 143 & Black & No & 3 \\
3 & M & Med & [45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 82; 84; 86; 88; 89; 91; 80; 83; 85; 87; 88; 89; 92; 86; 89; 93; 88; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125; 126; 127; 128; 129; 130; 131; 132; 133; 134; 135; 136; 137; 138; 139; 140; 141; 142; 143; 144; 145; 146; 147; 148; 149; 150; 151; 152; 153; 154; 155; 156; 157; 158; 159; 160; 161; 162; 163; 164; 165; 166; 166; 167; 168; 169; 170; 171; 172; 173; 174; 175; 176; 177; 178; 179; 180; 181; 182; 183; 184; 185; 186; 187; 188; 189; 190; 183; 189; 191; 184; 186; 187; 188; 189; 192; 189; 193; 194; 195; 196; 197; 198; 199; 200; 201; 2021; 203; 204; 205; 206; 207; 208; 209; 210; 211; 222; 223; 224; 225; 226; 227; 228; 230; 231; 232; 233; 234; 235; 236; 237; 238; 239; 240; 241; 242; 243; 244; 245; 246; 247; 248; 249; 250; 251; 252; 253; 254; 255; 256; 257; 258; 259; 260; 261; 262; 263; 264; 265; 266; 267; 268; 269; 270; 271; 272; 273; 274; 275; 276; 2777; 278; 279; 280; 281; 282; 283; 284; 285; 286; 287; 288; 289; 288; 289; 289; 290; 280; 281; 284; 286; 287; 288; 289; 281; 289; 289; 280; 282; 285; 287; 289; 281; 288; 289; 281; 289; 282; 284; 286; 288; 287; 289; 288; 289; 289; 291; 289; 292; 300; 301; 302; 303 to reach 0 with minimum generalizations) until zero violations. The search tree of Method2 (Greedy approach) is shown in Figure 5.  
As seen from Figure 5, the result is achieved after generating 3 tables, and when the violations become 0, the search stopped. In Figure 5, each node again is a table annotated by a corresponding heuristic value. Starting from the root node \(T(6)\) represents Table 1, with 6 violating rows. We see that after applying a generalization on Zip, Age and AC attribute, the resulting table has 2, 4 and 0 violating rows, respectively. The greedy solution produces Table 6 = \(T_{3}\), as a result. As shown in Table 6, there is no violation. However, the number of rows is 19, which is less than our solution which has 21 rows. However, the resulting table from Method 2 (Greedy search) is correct in that it satisfies the R. Therefore, even though Method 2 satisfies (2) it fails (1). Our proposed approach on the other hand satisfies both (1) and (2).