### Table 3: Comparing the LR and a MILP solver

"... In PAGE 16: ... Hence, the only fundamental difference between the two cases seemed to be whether a Quadratic Program (QP) or a Linear program (LP) was solved at each relaxation instead; since most often a QP can be solved in no more than three times the time it takes to solve an LP of the same size, we expected nothing more than an improvement of at most a factor of three in the running times, even less since the MILP formulation is significantly larger than the MIQP one. However we followed the advice of the referee, and the actual results, reported in Table3 proved us blatantly wrong. Columns RCDP have the same meaning as in the previous paragraphs; the results are however different since, having been obtained over an year after the previous ones, a more advanced and efficient version of the code was used, with a significant part of the performance improvements being due to using a more recent version of Mosek (version 5 vs.... ..."

### Table 1: Effect of Theorems 1 and 2 on size of MILP model for Example 1

2005

"... In PAGE 23: ...2% is a result of this flexibility provided by the stochastic program. Table1 compares the big-M reformulations of models P 1 and P 2 in terms of their sizes. The CPU time corresponds to the time required for these models to be solved using ILOG CPLEX 9.... ..."

Cited by 3

### Table 3: Comparison of Algorithm RSMAXT and an exact MILP-based solver for delay tolerance maximization.

2001

"... In PAGE 24: ... Our combined retiming and clock scheduling methodology is thus most promising for high-speed circuit design with a tight timing budget. Table3 compares the efficiency and effectiveness of the heuristic solver and the MIPS-based solver for a target clock of a2 a51 a0 a10a29 a0 a4 a13 . With a timeout limit set to 48 hours, the MIPS solver improves the tolerance of only a small number of circuits from our test suite.... ..."

### Table 1: Solving generic MILPs with SYMPHONY: Default settings and no a priori upper bound (summary)

2006

"... In PAGE 29: ... Strong branching was used to make branching decisions and the search strategy was a hybrid diving strategy in which one of the children of a given node was retained as long as its bound was within a given percentage of the best available. Table1 in the Appendix shows the results of the first set of experiments, in which SYMPHONY was run with default settings and no a priori upper bound. Detailed results... In PAGE 30: ... This eliminates redundant work, but the results still exhibit a very slight increase in the number of search nodes as the number of NP/CG modules is increased. This hurts the parallel efficiency, but the provision of an a priori upper bound still improves solution times across the board in comparison to those in Table1 . Note that the total amount of overhead, especially the ramp down and the idle time spent waiting for new node descriptions to be sent from the TM module are very significantly reduced for these runs over the runs with... In PAGE 43: ...2071 0.2977 Table1 0: Solving VRP instances with SYMPHONY: Default settings with heuristic upper bounds and global cut pool (summary) 4... In PAGE 44: ...5373 51.0083 Table1 1: Solving SPP instances with SYMPHONY: Default settings and no a priori upper bound (summary) 4... In PAGE 45: ...5373 51.0083 Table1 2: Solving SPP instances with SYMPHONY: Default settings and no a priori upper bound (32 NPs) 4... ..."

### Table 2: Clock period minimization with Algorithm RSMINP and an exact MILP-based branch-and-bound algo- rithm.

2001

"... In PAGE 21: ... To evaluate the relative speed and efficiency of our retiming and clock scheduling heuristic, we independently developed a MILP-based branch-and-bound solver. Table2 compares the runtimes and output clock periods of the two programs for a subset of our test suite. In general, the CPU requirements of the MILP-based optimizer grow very fast, due to the high computational complexity of mixed-integer linear programming.... In PAGE 21: ... With a 48-hour timeout, the MILP-solver runs out of time on most circuits, without having discovered a better solution than the heuristic scheme. The last column of Table2 shows the relative clock period improvement achieved by the MILP- based solver over our heuristic. Except for daio, the fastest circuit computed by the heuristic is as good as that of the MILP solver.... ..."

### TABLE 5. Use of reformulation.

Cited by 2

### Table 3: Scalability for generic MILP

2007

"... In PAGE 17: ... For all other runs, one hub was used. Table3 shows the results of these computations. Note that in this table, we have added an extra column to capture sources of overhead other than idle time (i.... In PAGE 19: ...he aggregated results are summarized in Table 5. Column P is the number of processors. Column Solver is the solver used. The other columns have the same meaning as those in Table3 . It can be seen from these results that BLIS scales reasonably well and the overhead is relatively small.... ..."

### Table 1: Classes of Query Reformulation

in Abstract

"... In PAGE 3: ...esearch question as possible. Authors were asked to approve our reformulations (i.e., con rm that the reformulated query corresponded to their intentions) or to correct the query, for resubmission to the pooling process. Table1 describes the four classes of query reformulation. We note that some number of the Cran eld queries were similarly reformulated (Cleverdon et al.... ..."

### Table 11: Hard instances : reformulated

in A Branch-and-Cut Algorithm for the Single Commodity Uncapacitated Fixed Charge Network Flow Problem

"... In PAGE 17: ... Also 8 Medium instances are now solved by all three systems. Detailed results for the hard instances can be found in Table11 in Annex B. From the above table we observe that all the Easy and Medium instances can be solved to optimality with the three systems.... In PAGE 26: ... The rest of the columns are grouped by system reporting the value of the LP after adding cuts at the top node, the value of the best IP solution found, the gap and the total time used by the system. Table11 reports the results for the hard instances after reformulation. The first column is the name of the instance, the second column is the class the instance belongs to.... ..."