### Table 1: Linear Programming Constraint Equations

### Table 1: Pruning results for similar length constraint (equation 1).

2002

"... In PAGE 3: ... The rst pruning method used the assumption that words from the same class will have similar lengths in terms of the widths of their bounding boxes. Thus, the following constraint was used to determine whether a given word is a possible match for a template: 1 templatelength imagelength (1) Table1 shows the results obtained with the similar length pruning constraint: Recall is the number of relevant words that were left after pruning at a given threshold value di- vided by the total number of relevant words. (a word image is relevant to the query if it has the same ASCII translation.... ..."

Cited by 1

### TABLE 2. Comparison between unbalanced and balanced constraint equations (Example 12).

2004

Cited by 2

### TABLE 2. Comparison between unbalanced and balanced constraint equations (Example 12).

2004

Cited by 2

### Table 2: Pruning results for similar area constraint (equation 2).

2002

Cited by 1

### Table 3 Here C is the constraint. Then the linear inequality constraint equations would be,

### Table 6 Constraint equations for the height one amino acid signatures in the training set

in The

2003

"... In PAGE 8: ...olution was to total 9. These equations are listed in Table 6. Notice that the individual constraint equations do not con- tain the majority of the variables. The two modulus equa- tions ( Table6 , Eqs. (16) and (23)) were incorporated into the system of equations by adding dummy variables (one for each modulus equation) to make them homogeneous.... ..."

### Table 6: Equations after Constraint Propagation

"... In PAGE 10: ...Table 6: Equations after Constraint Propagation Continuing constraint propagation yields the equations in Table6 , where D 1 =#28y =0^ z#3Ci#29. 2 Example 7 #28Example 6 Continued#29 Now consider the case when n #15 i.... In PAGE 10: ... Finally, it is easily seen that #28D i quot; ^ z#3Ci#29 quot; = D i quot; for i =0; 1. Inserting these observations | which all maybee#0E- ciently computed | in the equations of Table6 weget equations which after application of Boolean Simpli#0C- cation and Trivial Equation Elimination all simpli#0Ces to tt. Thus, in the case n #15 i, our minimization heuristics will yield tt as the property required of A in order that A j f B n satis#0Ces Y .... ..."

### Table 8. Equations after Constraint Propagation

1995

"... In PAGE 21: ... Using the propagation laws from Table 6 we get: tt #29 #10 y in Y 0 #11 #11 tt #29 #10 fy;zg in X 0 #11 #11 fy;zg in #10 D 0 #29 X 0 #11 where D 0 =#28y =0^ z = 0#29. This makes the implication D 0 #29 X 0 applicable to constraint propagation as follows: #28D 0 #29 X 0 #29 #11 D 0 #29 h #28z #15 i#29 _ #10 #5Bb#5D#28y in X 1 #29 ^88X 0 #11i #11 #10 D 0 #29 #5Bb#5D#28y in X 1 #29 #11 ^ #10 D 0 #2988X 0 #11 as #28z#3Ci^ D 0 #29=D 0 #11 #5Bb#5D #10 y in #28D 0 #29 X 1 #29 #11 ^88 #10 D 0 quot; #29 X 0 #11 Continuing constraint propagation yields the equations in Table8 , where D 1 = #28y =0^ z#3Ci#29. u t Example 9.... In PAGE 22: ... Finally, it is easily seen that #28D i quot; ^ z#3Ci#29 quot; = D i quot; for i =0; 1. Inserting these observations | whichallmay be e#0Eciently computed | in the equations of Table8 we get the simpli#0Ced equations in Table 9. Now, the conjuncts ff #29 #5Bc#5Dff are obviously equivalenttott andwillthus be removed by the boolean simpli#0Ccation transformations.... ..."

Cited by 85