### Table 3: Results for Branch-and-Bound (QP, 10-dim).

2007

"... In PAGE 20: ...3, which provides an upper bound for the problem (QA); Step 3 Running a branch-and-bound algorithm with the upper bound given in Step 2 to flnd the optimal solution for (QA). Table3 presents some randomly generated instances for the model (MVt). All these instances are 10 dimensional problems with 11 constraints.... ..."

### Table 4. The trace of AND/OR Branch-and- Bound search (#cm) versus the AOMDD size (#aomdd) for MAX-SAT pret instances.

"... In PAGE 13: ...ith problem classes pret and dubois from the SATLIB (http://www.satlib.org/) li- brary, which were previously shown to be difficult for 0/1 ILP solvers (CPLEX) [19]. Table4 shows the results for experiments with 8 pret instances. These are unsatis-... ..."

### Table 4. The trace of AND/OR Branch-and- Bound search (#cm) versus the AOMDD size (#aomdd) for MAX-SAT pret instances.

"... In PAGE 13: ...ith problem classes pret and dubois from the SATLIB (http://www.satlib.org/) li- brary, which were previously shown to be difficult for 0/1 ILP solvers (CPLEX) [19]. Table4 shows the results for experiments with 8 pret instances. These are unsatis-... ..."

### Table 5: Results of the truncated search with a limit of 30 minutes on the running time and no limit on the number of branch-and-bound nodes. Instances marked with an asterisk were solved to optimality.

2007

### Table 5: Benchmark results with IP branch-and-bound search in SICStus (FD/Q).

"... In PAGE 10: ....3.2 IP branch-and-bound in SICStus (FD/Q) While still in the FD framework, but now using an IP-style branch-and-bound search, we can improve the results signi cantly. Table5 shows the results of doing an branch-and-bound IP search in SICStus (FD/Q) with branching on fractional values of the solution to a series of linear relaxations. The downside of this is not directly obvious.... ..."

### Table 5: Benchmark results with IP branch-and-bound search in SICStus (FD/Q).

"... In PAGE 10: ....3.2 IP branch-and-bound in SICStus (FD/Q) While still in the FD framework, but now using an IP-style branch-and-bound search, we can improve the results signi cantly. Table5 shows the results of doing an branch-and-bound IP search in SICStus (FD/Q) with branching on fractional values of the solution to a series of linear relaxations. The downside of this is not directly obvious.... ..."

### Table 5: Benchmark results with IP branch-and-bound search in SICStus (FD/Q).

"... In PAGE 10: ....3.2 IP branch-and-bound in SICStus (FD/Q) While still in the FD framework, but now using an IP-style branch-and-bound search, we can improve the results signi cantly. Table5 shows the results of doing an branch-and-bound IP search in SICStus (FD/Q) with branching on fractional values of the solution to a series of linear relaxations. The downside of this is not directly obvious.... ..."

### Table 1: Execution times (in seconds) for branch-and-bound and exhaustive algorithms on zebrafish introns

2002

"... In PAGE 7: ... This may not seem very fast, but we should consider the fact that the calculation with this pattern class would not have been feasible without the pruning of the search space. Table1 shows the comparison of execution times for the zebrafish introns, with and without the branch-and-bound search, while varying the maximum length of the pattern searched for (the length of a VLDC pattern is defined as the number of non-wild card characters). The run time for the exhaustive search is exponential as expected while the run time for the branch-and-bound algorithm seems to converge, even showing a slight decrease when not specifying a maximum length.... ..."

Cited by 8

### Table 1: Execution times (in seconds) for branch-and-bound and exhaustive algorithms on zebra sh introns

2002

"... In PAGE 7: ... This may not seem very fast, but we should consider the fact that the calculation with this pattern class would not have been feasible without the pruning of the search space. Table1 shows the comparison of execution times for the zebra sh introns, with and without the branch-and-bound search, while varying the maximum length of the pattern searched for (the length of a VLDC pattern is de ned as the number of non-wild card characters). The run time for the exhaustive search is exponential as expected while the run time for the branch-and-bound algorithm seems to converge, even showing a slight decrease when not specifying a maximum length.... ..."

Cited by 8