### Table 2Lagrangian and Linear Programming Relaxations Lagrangian LB Strong LP

2000

"... In PAGE 12: ... For these instances, the Lagrangian approach requires a maximal computation time of less than 9 minutes (537 seconds), which is in sharp contrast to the 72 hours needed by Brucker and Knust (2000). Table2 compares the Lagrangian approach to the corresponding linear programming relaxation (2), (3), (4), (8), and (9), again based on the ProGen instances Table 1 Comparison of Quality and Computation Times for Lower Bounds Lagrangian LB+(14) Brucker and Knust # jobs # inst. Dev.... In PAGE 13: ... It turns out that the primal simplex method solves this linear programming relaxation much faster than the barrier method does. With the barrier method, the instances with 120 jobs could not be solved in reason- able time, hence the data is missing in Table2 . More importantly, these computation times are, in fact, dras- tically higher than the computation times required to (approximately) solve the Lagrangian dual.... ..."

Cited by 17

### Table 7: NJA and the Alternating Directions method for quadratic problems

1995

### Table 20: Comparable time bounds for alternative 1, data copying methods

"... In PAGE 50: ... The measured values in Table 17 are used to calculate the probable transmission time. In Table20 , these calculated values are shown. The values in the table are calculated applying the simplified model in Equation 2.... In PAGE 50: ...Table 20: Comparable time bounds for alternative 1, data copying methods Please notice that the values in Table20 are not calculated with consideration to the requirement of the switching capacity. Those values are only used to compare the methods for solving this sub-domain.... In PAGE 51: ... If alternative 1, namely copying the data directly from the slave memory, is used it will take 1.76 seconds to perform the data copying part of the program, see Table20 . If the slave memory is copied via the VME memory instead, it will take 1.... ..."

### Table 7 Comparison of Linear Programming and Lagrangian Lower Bounds Weak LP Lagrangian LB

2000

"... In PAGE 17: ... Our results on the remaining instances are reported in Uetz(2001). Table7 compares the weak linear programming relaxation (2), (4), (6), (8), and (9) to results ob- tained with the Lagrangian approach. Note that the computation times for solving the strong linear pro- gramming relaxation (2), (3), (4), (8), and (9) are pro- hibitively high for the larger of these benchmark instances, for both primal and dual simplex and the barrier code of ILOG CPLEX.... ..."

Cited by 17

### Table II. Cycles in Original and Augmented Benchmark Graphs. Results are given for the three different methods of encoding transitivity constraints. Circuit Direct Dense Sparse

2000

Cited by 30

### Table II. Cycles in Original and Augmented Benchmark Graphs. Results are given for the three different methods of encoding transitivity constraints. Circuit Direct Dense Sparse

2000

Cited by 30

### Table I. Basic terms and notation for linear (LP), semidefinite (SDP), and conic programming. Term LP SDP Conic Notation

2005

Cited by 11

### Table 3: Bounds from Semidefinite Programming. (Intel Pentium III, 933 MHz). 30

2004