### TABLE I Computational Complexity of Various Problems of Survivable Access Network Design

### TABLE I Computational Complexity of Various Problems of Survivable Access Network Design

### Table 3: Multicommodity Flow Survivable Network Design: Network Statistics.

2003

"... In PAGE 23: ...ity pattern. Its constraint matrix has dual block-angular structure. Each diagonal block in it is a multicommodity flow problem for some reduced network. We report in Table3 several network characteristics for the test problems: graph sizes and data for original routings (Routes), the number of failures and the number of conditional demands created by them. The latter is a major factor that determines the overall size of the LP formulation (16) of this problem.... ..."

Cited by 18

### Table 3: Multicommodity Flow Survivable Network Design: Network Statistics.

2000

"... In PAGE 23: ...ity pattern. Its constraint matrix has dual block-angular structure. Each diagonal block in it is a multicommodity flow problem for some reduced network. We report in Table3 several network characteristics for the test problems: graph sizes and data for original routings (Routes), the number of failures and the number of conditional demands created by them. The latter is a major factor that determines the overall size of the LP formulation (16) of this problem.... ..."

### Table 4: Multicommodity Flow Survivable Network Design: Solution Statistics.

2003

"... In PAGE 23: ... The sizes of several test problems and the solution statistics for two solvers, our structure exploiting code and Cplex 6.0 barrier code, are reported in Table4 . To facilitate the comparison we ran both solvers on the same Linux PC with 300 MHz Pentium Pro processor and 384 MB of RAM.... In PAGE 24: ...0 Table 6: Single-commodity Flow Survivable Network Design: Solution Statistics. The analysis of results collected in Table4 reveals that the structure exploiting code is slightly faster than Cplex on these problems. Both codes show slow increase of the number of iterations with the size of the problem.... ..."

Cited by 18

### Table 4: Multicommodity Flow Survivable Network Design: Solution Statistics.

2000

"... In PAGE 23: ... The sizes of several test problems and the solution statistics for two solvers, our structure exploiting code and CPLEX 6.0 barrier code, are reported in Table4 . To facilitate the comparison we ran both solvers on the same Linux PC with 300 MHz Pentium Pro processor and 384 MB of RAM.... In PAGE 24: ...0 Table 6: Single-commodity Flow Survivable Network Design: Solution Statistics. The analysis of results collected in Table4 reveals that the structure exploiting code is slightly faster than CPLEX on these problems. Both codes show slow increase of the number of iterations with the size of the problem.... ..."

### Table 5: Single-commodity Flow Survivable Network Design: Network Statistics.

2003

"... In PAGE 24: ... This problem has a less regular structure, with one multicommodity block and many small single-commodity blocks. Network characteristics of the test examples are given in Table5 and the sizes of the corresponding linear programs are given in Table 6. Since the sizes of these problems vary from small to medium we solved them also with the Cplex default (primal) simplex method.... ..."

Cited by 18

### Table 1 below summarizes the lower bounds for all of the above problems, with degree of fault tolerance

1996

"... In PAGE 14: ... Table1 : Lower bounds on the star network. The algorithms derived here for all of the above problems are optimal in terms of time and number of message transmissions.... ..."

Cited by 13

### Table 5: Single-commodity Flow Survivable Network Design: Network Statistics.

2000

"... In PAGE 24: ... This problem has a less regular structure, with one multicommodity block and many small single-commodity blocks. Network characteristics of the test examples are given in Table5 and the sizes of the corresponding linear programs are given in Table 6. Since the sizes of these problems vary from small to medium we solved them also with the CPLEX default (primal) simplex method.... ..."

### Table 1: Design variable bounds for the ACS problem.

in Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data

"... In PAGE 12: ... The optimization of this problem was carried out using the CSSO data base generation approach in Step 9 of the algorithm. The starting point for this problem is given in the third column of Table1 . The algorithm converged to the global optimum given in Table 2 in four approximate minimizations as observed in the convergence plot of Fig- ure 3.... In PAGE 12: ... The constr function is an implementation of the sequential quadratic programming (SQP) algorithm (see Grace (1992)). The starting point given in Table1 was supplied to the MAT- LAB function constr, which required 52 high delity anal-... ..."