### Table 4. Results for pret MAX-SAT problem instances.

2007

"... In PAGE 13: ...ig.3. Results for dubois MAX-SAT problem instances. toolbar3 [20], a classic OR Branch-and-Bound algorithm that solves MAX-SAT as a Weighted CSP problem, and PBS [21], a specialized pseudo-Boolean optimizer. Table4 shows the results for experiments with 6 pret instances. These are unsat- isfiable instances of graph 2-coloring with parity constraints.... ..."

Cited by 1

### Table 1: Known upper bounds for MAX-SAT and MAX-2-SAT

"... In PAGE 1: ... Moreover, it is known [15] that the decision version of MAX-2- SAT is NP-complete, if each variable appears in an in- put formula at most three times. In Table1 we give the best known upper bounds for MAX-SAT and MAX-2- SAT w.... In PAGE 1: ... For simplicity, throughout all the paper we give exponen- tial upper bounds without polynomial factors. Almost all algorithms from Table1 (as well as our new algo- rithm) are based on a splitting method and thus use polynomial space. The only exception is the algorithm by Williams [16], which is based on di erent ideas ( nd- ing triangles in an auxiliar graph) and uses exponential space.... ..."

### Table 3: Results of the Max-SAT experiment

2002

"... In PAGE 14: ... 5.5 Results for Max-SAT Benchmarks The results of the Max-SAT experiment are shown in Table3 . For each unsatisfiable instance the table lists the instance name and size (number of variables |V| and clauses |C|), the size of the corresponding companion satisfi- able instance (i.... ..."

Cited by 36

### Table 3: Results of the Max-SAT experiment

2002

"... In PAGE 6: ... 5.5 Results for Max-SAT Benchmarks The results of the Max-SAT experiment are shown in Table3 . For each unsatisfiable instance the table lists the instance name and size (number of variables |V| and clauses |C|), the size of the corresponding companion satisfiable instance (i.... ..."

Cited by 36

### Table 3: Results of the Max-SAT experiment

"... In PAGE 6: ... 5.5 Results for Max-SAT Benchmarks The results of the Max-SAT experiment are shown in Table3 . For each unsatisfiable instance the table lists the instance name and size (number of variables |V| and clauses |C|), the size of the corresponding companion satisfiable instance (i.... ..."

### 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 3. Results of the Max-SAT experiment. Unsat instance Symmetry statistics PBS time

"... In PAGE 11: ... The Max-SAT and Max-ONEs instances were constructed as shown in [1]. The results for the Max-SAT and Max-ONEs experiments are listed in Table3 and Table 4, respectively. Both tables indicate the size of the original CNF formula.... In PAGE 11: ... The runtimes for solving original instances and instances augmented with SBPs are also shown. in Table3 indicates the minimum (i.... ..."

### Table 1: Comparing the e ciency of various MaxSat algorithms with respect to the exponential terms involved.

1998

Cited by 5

### Table 1. Performance comparison of ILS-YI, GLSSAT2, and SAPS over a range of unweighted MAX-SAT test sets. The precise meaning of the step and time performance is explained in the text, CPU times are measured in CPU milliseconds. The speedup factor s.f. shows the improve- ment in time performance of SAPS over GLSSAT2. The fraction of best measure f.b. indicates the fraction of instances within the respective test-sets for which SAPS performs better than GLSSAT2 in terms of CPU time. For SAPS, default parameters settings of (a8 ,a5a48a9 a11a14a13a15a13a68a16 a18 ,a0 a20a28 )a21

2003

"... In PAGE 7: ... In all cases, the solution qualities thus obtained could not be improved upon with any method we are aware of (including SAPS), and in several cases their optimality was confirmed by the complete maxsat solver (which took several CPU days). As we will demonstrate in Table1 , GLSSAT2 consistently outperforms ILS-YI, and so we compare the performance of SAPS primarily with that of GLSSAT2. Our first comparison between SAPS and GLSSAT2 is shown in Figure 3, where we compare the search step performance and time performance of the two algorithms on the jnh problem instances.... In PAGE 9: ... From this figure, it is clear that SAPS outperforms GLSSAT2 for these test sets in terms of both search steps (left) and CPU time (right) required for finding quasi- optimal solutions. In Table1 we summarise the results from our experiments on all test sets used in this study. For each problem instance, at least 100 runs of each algorithm were performed, in each of which a quasi-optimal solution was found.... ..."

Cited by 4