### Table 1 Main results for IMFP, IMCP and their subproblems IMFP IMCP UnSplitFlow CapPath EdgeDisjPath Multiterminal

2001

"... In PAGE 13: ....-C. Costa et al. / European Journal tiflow problems, and of their subproblems, is often in planar graphs, the multiterminal cut and inte- gral flow problems in acyclic graphs and the multicut and integral flow problems in directed trees. Finally, we would like to point out that there are still some interesting opened questions: what is the complexity of the two flow problem in directed bipartite graphs? Is it possible to approximate within a constant ratio the minimum multicut problem in unrestricted graphs? To conclude this survey, we give Table1 which summarizes the most significant results. References [1] R.... ..."

### Table 1: Node counts and time for instances of multi-commodity network ow problems CPLEX CPLEX + CUTS

2007

"... In PAGE 126: ... CPLEX branch-and-bound was used to solve the two mixed integer programming formulations. Table1 1: Comparison of two formulations: lower and upper bounds were returned at the end of 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 127: ... This shows that as an integer programming formulation, with no additional cuts or heuristics added, formulation (P 2) performs better than formulation (P 1). Table1 2: Comparison of two formulations: Node counts and solve times (P1) (P2) Prob Node Count Time Node Count Time E10 10 240 1.5 56 0.... In PAGE 128: ... The time limit was 300s, so if optimal solution is not found in the allotted time for a problem the corresponding entry for solve time is 300s and node count entry is the number of nodes explored in 300s. Table1 3: Comparison of two formulations with cutting planes and heuristics: lower and upper Bounds after 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 128: ...00 0.00 Entries in bold represent that optimal solution was found in 300 second Looking at the results from Table1 3, we can see that, with the help of cuts and heuristics, formulation (P 1) was able to provide better results than (P 2). More problems were solved to optimality and for except one, the bounds provided for the problems not solved to optimality in allotted time by formulation (P 1) were stronger than formulation (P 2).... In PAGE 129: ...Table1 4: Comparison of two formulations with cutting Planes and heuristics: node counts and computation times (P1) (P2) Prob Node Count Time Node Count Time E10 10 0 4.01 0 0.... ..."

### Table 1: Time with and without cuts SETS CONS VARS NO CUTS CUTS NO CUTS CUTS

2000

"... In PAGE 8: ...Table1 has for each problem size the average CPU time in seconds with and without cut generation to obtain a proven optimal solution and the rst feasible solution. Table 2 has for each problem size the average number of nodes processed with and without cut generation, as well as the number of cuts generated, to obtain a proven optimal solution and the rst solution.... ..."

Cited by 6

### Table 14. Cuts per node in the branch and cut tree of problem

1997

Cited by 12

### Table 1: Cuts generated for problems in Table 6

1998

"... In PAGE 16: ... To give an idea about the relative importance of the valid inequalities, we next present the details of the cuts generated for some of the problems we studied. In Table1 , n-Cut is the percentage of cuts generated by the n-Cut heuristic. 3-Part is the percentage of cuts generated by the n-Partition heuristic for n 3.... ..."

Cited by 43

### Table 1: Cuts generated for problems in Table 6

1998

"... In PAGE 16: ... To give an idea about the relative importance of the valid inequalities, we next present the details of the cuts generated for some of the problems we studied. In Table1 , n-Cut is the percentage of cuts generated by the n-Cut heuristic. 3-Part is the percentage of cuts generated by the n-Partition heuristic for n 3.... ..."

Cited by 43

### Table 5: Memoryless Results for Cutting Stock Problems

2003

"... In PAGE 14: ... This meant that the initial matrix entries were left undisturbed throughout the run. The results of these runs are shown in Table5 for the cutting stock problems and Table 6 for the bin packing problems (up to size 4000). Prob HACO No memory avg best time avg best time 6a 79.... ..."

Cited by 3

### Table 5 Memoryless results for cutting stock problems

"... In PAGE 10: ... This meant that the initial matrix entries were left undisturbed throughout the run. The results of these runs are shown in Table5 for the cutting stock problems and Table 6 for the bin packing problems (up to size 4000). It is clear from these results that the local search procedure can solve small problems but needs the ACO procedure when larger problems are encountered.... ..."

### Table 14: Numerical results on maximum cut problems.

1997

Cited by 25

### Table 2: Nodes and cuts

2000

"... In PAGE 8: ...generation to obtain a proven optimal solution and the rst feasible solution. Table2 has for each problem size the average number of nodes processed with and without cut generation, as well as the number of cuts generated, to obtain a proven optimal solution and the rst solution. For those problems that were not solved to optimality we included in the averages of table 2 the number of nodes processed (50,000) when the algorithm was halted, as well as the computational time spent so far in the time averages of table 1.... ..."

Cited by 6