### Table 3. Due to the small super-row O-space, even BnB alone can solve the instance n = 13 in around 5 minutes. ORDS finds the optimal value for n = 16 in 245 minutes with merely 11002 backtracks. To the best our knowledge, this is the largest instance solved with complete branch and bound search on a pure CSP model. Indeed, our answer is the only witness to the optimal value reported by (Larrosa, Morancho, amp; Niso 2005).

"... In PAGE 6: ... Table3 : Results on super-row model: O-vars. Conclusion Constraint optimization problems are commonly solved by a (simple) branch and bound search on the problem variables.... ..."

### Table 3: The witness

"... In PAGE 12: ...ontains wait locations (i.e., locations to which automata for Sender and Re- ceiver can get in, if actions wait 1 and wait 2 are performed). We have done such a reachability test, and we found a witness of length 46 which shows that both Sender and Receiver can both move to a waiting state, and there is no way for them to move to a ready state; for this witness see Table3 ; experimental results are presented in Table 4. The reason the modified Java program may go into an infinite loop can be found by examining the witnesses for the reachability property mentioned above: the Sender can continuously send messages, but he never gets an acknowledge- ment.... ..."

### Tableaux and witnesses for the -calculus

1995

Cited by 2

### Table 1. Comparison of results for various approaches.

"... In PAGE 8: ... 4. Numerical Results Table1 compares the balance and uniformity (t,s) of (n,2) de Bruijn sequences... In PAGE 9: ... In the case of Algorithm II, the characteristics of the sequences obtained by the optimal mappings with respect to both balance and uniformity criteria are shown. ------------------------- Table1 goes here ------------------------- In Table 1, we observe that: 1. Although Algorithm I generates sequences with optimal uniformity (minimum s), the corresponding balance criterion t is rather large.... In PAGE 9: ... In the case of Algorithm II, the characteristics of the sequences obtained by the optimal mappings with respect to both balance and uniformity criteria are shown. -------------------------Table 1 goes here ------------------------- In Table1 , we observe that: 1. Although Algorithm I generates sequences with optimal uniformity (minimum s), the corresponding balance criterion t is rather large.... ..."

### Table 1. Performance Characteristics of Different AM Implementations

1997

"... In PAGE 7: ...ficient, buffered writes in the SCI DSM only. Performance measurements on the UCSB SCI cluster show competitive performance behavior of the SCI AM system ( Table1 ). Our own implementation, depicted in the first row of Table 1, adds little over- head to the raw latency of 9.... ..."

Cited by 13

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 2: Technology Mapping results

"... In PAGE 8: ... The results show that the Boolean approach reduces the number of matching algorithm calls, nd smaller area circuits in better CPU time, and reduces the initial network graph because generic 2-input base function are used. Table2 presents a comparison between SIS and Land for the library 44-2.genlib, which is distributed with the SIS package.... ..."

### Table 1: Comparison results a sequential implementation, was slower than Monahan apos;s method but faster than the witness algorithm, especially in the 4 4 maze which is the most time consuming problem. We must say, however, that the code of our NN approach is not yet optimized while the other algorithms are indeed. A decrease in processing time is expected for the NN technique once the code will be optimized. In addition, NN o ers an inherent parallelism, which may lead to e cient hardware implementations.

"... In PAGE 7: ...tp://ftp.es.ele.tue.nl/pub/lp solve. The results obtained are displayed in Table1 , where the total CPU time, the number of iterations, the number of support lines (optimal ~ vectors) and the discount parameter used are shown. The value used to stop the time iterative process was 1 10?9 in all cases.... ..."

### Table 2 Outer loop of the witness algorithm.

1998

"... In PAGE 19: ... This is because maximizing over actions and then policy trees is the same as maximizing over the pooled sets of policy trees. The code in Table2 outlines our approach to solving pomdps. The basic structure remains that of value iteration.... ..."

Cited by 451

### Table 2 Outer loop of the witness algorithm.

1998

"... In PAGE 19: ... This is because maximizing over actions and then policy trees is the same as maximizing over the pooled sets of policy trees. The code in Table2 outlines our approach to solving pomdps. The basic structure remains that of value iteration.... ..."

Cited by 451