### Table 1 Bounds on the performance guarantee

"... In PAGE 5: ... For instance, in a graph with no cycle longer than 5, the analysis bounds the performance guarantee (when k = 5) by 1:464. Table1 gives lower and upper bounds on the performance guarantee of the algo- rithm for small values of k and in the limit as k ! 1. The lower bounds are shown... In PAGE 10: ... For instance, for c = 3, by following the proof of Theorem 4.1, one can show that this would improve the performance guarantee of Contract-Cyclesk to ck ? 1=36 (for k 4), matching the lower bound in Table1 . (The lower bound given holds for the modi ed algorithm.... ..."

### Table 1: performance guarantees: BV

"... In PAGE 115: ...Table 1: performance guarantees: BV C4CB D1CPDC BPC7C8 CC same machine, then the swap neighborhood is empty; therefore, we define the swap neighborhood as one that consists of all possible jumps and all possible swaps. As can be seen in Table1 , the jump and swap neighborhoods have no constant performance guarantee for C9CZBV D1CPDC . Therefore, we introduce a push neighborhood, for which any local optimum is at most a factor BE A0 BE D1B7BD of optimal for C9CZBV D1CPDC .... In PAGE 115: ... When pushing all jobs on the critical machines is unsuccessful, we are in a push optimal solution. In Table1 the performance guarantees for the various local optima and scheduling problems are given. UB = AQ denotes that AQ is a performance guarantee and LB = AQ denotes that the performance guarantee cannot be less than AQ; AQ denotes that UB = LB = AQ.... In PAGE 121: ...Empty Out-tree To approximate solution 0,079 0,005 Tolower bound 0,115 0,318 Table1 : Average relative errors of approximate solution of algorithm based on y jt -formulation to approximate solution of algorithm based on x jt -formulation and lower bound ( = 1). The graph of precedence constraints Empty Out-tree To approximate solution 0,048 0,001 Tolower bound 0,073 0,309 Table 2: Average relative errors of approximate solution of algorithm based on y jt -formulation to approximate solution of algorithm based on x jt -formulation and lower bound ( =1= p 2).... ..."

### Table 4: Performance guarantees of the GLSA with arbitrary priority.

### Table 10: MAX-3-SAT, 20 variables, observed performance guarantee

2005

"... In PAGE 27: ...Zwick is defined as the average number of clauses satisfied in a try divided by the upper bound obtained by their SDP. Table10 gives the average over the instances of the observed performance guarantees of the different approaches. Table 9 shows a trend break from density 7.... ..."

Cited by 1

### Table 5.17: Performance guarantee of (LOP) provided by (lop) (railroad)

### Table 6: Percentage execution time degradation for performance-guaranteed memory algorithms.

2004

"... In PAGE 8: ...2.2 Performance Guaranteed Algorithms Table6 shows the performance degradation for the 8 algorithms that use the performance guarantee method described in Section 3. Slowdownlimit ranges from 5% to 30%.... ..."

Cited by 11

### Table 5: Percentage execution time degradation for performance-guaranteed memory algorithms.

2004

"... In PAGE 8: ...2.2 Performance Guaranteed Algorithms Table5 shows the performance degradation for the 8 algorithms that use the performance guarantee method described in Section 3. Slowdownlimit ranges from 5% to 30%.... ..."

Cited by 11

### Table 6: Percentage execution time degradation for performance-guaranteed memory algorithms.

2004

"... In PAGE 8: ...2.2 Performance Guaranteed Algorithms Table6 shows the performance degradation for the 8 algorithms that use the performance guarantee method described in Section 3. Slowdownlimit ranges from 5% to 30%.... ..."

Cited by 11

### Table 10 MAX-3-SAT, 20 variables, observed performance guarantee d

2007

"... In PAGE 34: ... The observed performance guarantee of the approach of Karloff and Zwick is defined as the average number of clauses satisfied in a try divided by the upper bound obtained by their SDP. Table10 gives the average over the instances of the observed performance guarantees of the different approaches. Table 9 shows a trend break from density 7.... ..."

Cited by 1