### Table 2: Results for medium-size task graph examples

2007

"... In PAGE 7: ... Medium-size examples seem to be difficult even for packing formulation. Results given in the Table2 show that more that 24 hours are needed for most of them to be solved to the optimality. Namely, for these examples we set time limit of 24 hours for the CPLEX execution.... In PAGE 7: ... Namely, for these examples we set time limit of 24 hours for the CPLEX execution. In the fourth column of Table2 we put the required execution time to obtain the optimal solution (if it has been reached) or the given time limit (if the optimal solution remind unfound). The last columns contains the gap between the final solution and the obtained lower bound.... ..."

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### Table 2: medium-sized problems

"... In PAGE 16: ...nstalled network capacity. In our example, hT = 2.0, which is calculated based on the assumption of a 7% continuous cash flow growth after the planning horizon. In Table2 we describe basic properties of the medium-sized data sets and the resulting instances of MULTIREV. Here the last two columns show the minimum and maximum number of paths per node pair.... In PAGE 17: ...2 Comparison to other solvers In order to evaluate our algorithm we compared it against LOQO [30] and SNOPT [17], two well-known and highly regarded general-purpose nonlinear solvers. Recall that Table2 describes statistics on the optimization problems. In Table 9 we show the performance comparison of our algorithm and solvers on these problems.... ..."

### Table 4.2 Statistics for the medium sized office scene. Even simpler form factor tasks can lead to a nearly linear speedup.

### Table 4: Final results for the small- and medium-size circuits.

1994

"... In PAGE 25: ... These results re ect the e ectiveness of procedure pack together as a post-optimization component of algorithm TS-CPP. We give in Table4 the results obtained for the small- and medium-size circuits for L = 15; 17; 20 by algorithms mrl (Roberts and Lala [32]), cep (Davis-Moradkhan [12] and Davis- Moradkhan and Roucairol [14]) and TS-CPP (using algorithm cep for the generation of the initial solution). For each circuit and each algorithm, we present the number of subcircuits, the number of cuts and the ratio between the number of cuts and the total number of logical gates and outputs in the circuit.... ..."

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### Table 2: Results for the medium-size circuits with L = 15. 21

1994

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### Table 3: Results for the medium-size circuits with L = 20. 22

1994

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### Table 1 Privatization routes for medium-size and large enterprises

"... In PAGE 15: ... Having evolved from central planning apos;s need to economize on transaction costs, many are monopolies. Table1 summarizes the various methods used by the more advanced reformers to privatize medium and large industrial firms and estimates the extent of privatization in each country under each method.6 What lessons have emerged from attempts to privatize this important yet problematic sector? A.... In PAGE 19: ... The other countries, which lacked a benefactor of West Germany apos;s economic strength, could only move slowly-or adopt radically different divestiture techniques. In 6 years (1990 through 1995) Hungary was able to transfer only about 40 percent of its state-owned assets to private hands through formal sales programs ( Table1 , and Pistor and Turkewitz, 1996). With extensive assistance from former Treuhandanstalt officials, Estonia sold most of its enterprises in three years (1992-95).... ..."

### Table 2: Parameter Values for a Medium-Size Web Table

### Table 1: SPP: Small and medium size instances

in Group Updates and Multiscaling: An Efficient Neural Network Approach to Combinatorial Optimization

1996

"... In PAGE 21: ... The average value of the nal annealing temperature over all experiments with the ne-scale network was 1:74. The results obtained from the experiments are shown in Table1 for small and medium size instances and in Table 2 for big size instances. As a metric of the quality of a feasible solution obtained for a given instance I of the problem we use the approximation ratio which is de ned as h(I)=opt(I), where h(I) denotes the cardinality of the obtained feasible solution and opt(I) denotes the cardinality of the optimal solution [17].... In PAGE 23: ...) Since, due to the problem formulation, just one execution of the p-net is adequate to obtain near-optimal solutions, this bene t is signi cantly higher than the overhead imposed by the construction of the p-net and by the fact that the annealing starts at a higher temperature. As Table1 indicates, the average speedup for small and medium size instances was in the range between 2 and 18, while for large instances the speedup could not be determined, as the big size of the ne-scale network did not allow us to nd acceptable solutions in reasonable time (Table 2). It should also be noted that the quality of the obtained solution depends heavily on the choice of the temperature reduction rate.... ..."

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### Table 2: Duplicate Detection with Medium Sizes of Queries

2000

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