### Table 2: Efficiency of the Lagrange optimization procedure for BU BPBIand BK.

2004

"... In PAGE 18: ... In the absence of an analytical expression for the number of iterations required to arrive at a solution, we demonstrate the efficiency of the proposed procedure empirically. In Table2 , we list the total number D4 BU B4CF B5 of unique TAM partitions for a total TAM width of CF and for BU TAMs. The value of D4 BU B4CF B5 is calculated using the expression D4 BU B4CF B5 BP CF BUA0BD BUAXB4BUA0BDB5AX [12].... ..."

Cited by 4

### Table 1: Efficiency of Lagrange procedure for BU BPBIand BK.

"... In PAGE 4: ... In the absence of an analytical expression for the number of iter- ations required to arrive at a solution, we demonstrate the efficiency of the proposed procedure empirically. In Table1 , we list the total number D4 BU B4CFB5 of unique TAM partitions for a total TAM width of CF and for BU TAMs. The value of D4 BU B4CFB5 is calculated using the expression D4 BU B4CFB5BP CF BUA0BD BUAXB4BUA0BDB5AX [8].... In PAGE 4: ... Note that this expression is accurate only for larger values of CF; hence we present results only for CF AL BGBG. In Table1 , we compare the efficiency of the La- grange optimization algorithm with that of the Partition evaluate algorithm proposed to solve Problem C8 C6C8BTCF in [8]. The efficiency AH is calculated as the ratio of the number of TAM partitions evalu- ated by the Lagrange optimization procedure to the total number of unique partitions.... ..."

### Table 1: Efficiency of Lagrange procedure for BU BPBIand BK.

"... In PAGE 4: ... In the absence of an analytical expression for the number of iter- ations required to arrive at a solution, we demonstrate the efficiency of the proposed procedure empirically. In Table1 , we list the total number D4 BU B4CFB5 of unique TAM partitions for a total TAM width of CF and for BU TAMs. The value of D4 BU B4CFB5 is calculated using the expression D4 BU B4CFB5BP CF BUA0BD BUAXB4BUA0BDB5AX [8].... In PAGE 4: ... Note that this expression is accurate only for larger values of CF; hence we present results only for CF AL BGBG. In Table1 , we compare the efficiency of the La- grange optimization algorithm with that of the Partition evaluate algorithm proposed to solve Problem C8 C6C8BTCF in [8]. The efficiency AH is calculated as the ratio of the number of TAM partitions evalu- ated by the Lagrange optimization procedure to the total number of unique partitions.... ..."

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 5 shows results on a subset of all test instances indicating the strength of the various separation routines. To concentrate on the influence of the separation procedures on the lower bound only, an optimal solution was supplied as input sequence. Column ALL gives the results when all separation routines are used. The first entry corresponds to the optimality gap at the root node (o ijj 100), the second entry to the overall time (min.sec) to solve the instance to optimality. In the last row gaps and computing times are summed up. It turns out that the most efficient separation routines are those for rr-, er-, and (i a) inequalities. omputing times considerably increase if these procedures are not used. hey

in A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints

1997

### Table 1: Time costs of the procedures in the sequential BH algorithm Procedure Time

"... In PAGE 7: ... To measure the relative cost of each step in the sequential BH algorithm, a number of runs were performed to estimate the efficiency of the sequential BH algorithm and the fraction of time each step of the algorithm takes. In Table1 we show the time costs of the main steps of the sequential BH algorithm when run on a single workstation for 16,000 particles and 1000 time steps. As the Table 1 shows, most of the computation is incurred by CalcForces procedure which is about 96% of the total execution time of the algorithm.... In PAGE 7: ... In Table 1 we show the time costs of the main steps of the sequential BH algorithm when run on a single workstation for 16,000 particles and 1000 time steps. As the Table1 shows, most of the computation is incurred by CalcForces procedure which is about 96% of the total execution time of the algorithm. This alerts us that performance optimization techniques should focus on this step.... In PAGE 19: ... 61 3.4 Tree Traversal once for each processor domain From the run time cost analysis of the BH algorithm shown in Table1 , the CalcForces procedure takes more than 96% of the total run time of the algorithm. So, one of the ways to optimize the algorithm is to optimize the CalcForces procedure.... ..."

### Table 1: Density Efficiency Efficiency,

1996

"... In PAGE 12: ... Marron and Wand 1992 list 15 normal mixture densities showing some of the wide range of variations that are obtainable with simple mixtures. Table1 shows the efficiency of the FKE for these densities. The SKE bandwidth is chosen to be optimal (asymptotically) under the mixture assumption.... ..."

Cited by 6

### Table 1: Density Efficiency Efficiency,

"... In PAGE 12: ... Marron and Wand 1992 list 15 normal mixture densities showing some of the wide range of variations that are obtainable with simple mixtures. Table1 shows the efficiency of the FKE for these densities. The SKE bandwidth is chosen to be optimal (asymptotically) under the mixture assumption.... ..."

### Table 4 - Efficiency of Different Protocols Using Standard ATM Procedures

1991

"... In PAGE 9: ...2. Efficiency of Standard Procedures Table4 shows the transmission efficiency of four protocol combinations. The SMDS-802.... In PAGE 10: ...ead. However, cell padding causes efficiency to respond abruptly to changes in overhead. That is, efficiency is insensitive to large variations in certain protocol design dimensions, and sensitive to small variations in others. Table4 shows that moving from SMDS, with 28 bytes of overhead, to MSP, with 8 bytes of overhead, improves application efficiency by only 2.8%.... ..."

Cited by 15

### Table B - Datagram Efficiency Using Standard ATM Procedures

1991

Cited by 15