### TABLE 3 Numerical Comparisons of Performance and CPU Consumption on GAPs with Small Al.The MFA Algorithm ia Checked Against an Exact DBB Method and a Polynomial-time Algorithm (MTG) for Approximate Solutiona. All the Testa were Carried Out on a DEC Alpha 30001400Workstation

1996

### Table 1 summarizes our results. For conciseness, in the table below when we indicate that a problem is c-hard we mean that, unless NP = ZPP, no polynomial time algorithm can approximate it to within a factor of c.

"... In PAGE 5: ... Table1 : Approximation bounds and inapproximability results for each problem. 1.... ..."

### Table 3: Numerical comparisons of performance and CPU consumption on GAP apos;s with small N. The mean eld (MF) algorithm is checked against an exact depth- rst and branch-and-bound (DBB) method and a polynomial-time algorithm (MTG) for approximative solutions. All the test were made on a DEC Alpha 3000/400 workstation.

"... In PAGE 13: ... [8]). Table3 shows the result for small N problems where one can compare against the exact solutions. The numbers shown are averages over 1000 independent runs.... ..."

### Table 2: Our Results: (in-)approximability via deterministic (equilibria-)truthful mechanisms for identical machines. ki denotes the number of jobs owned by agent i and k = maxi ki; lower bounds apply to exponential-time mechanisms as well, while upper bounds are provided via polynomial-time mechanisms.

"... In PAGE 5: ... Motivated by this negative result, we turn our attention to truthful approximate mechanisms and give upper and lower bounds on the approximation ratio of such mechanisms. The results are summarized in Table2 . Some of our positive results are obtained via new polynomial-time approximation algorithms which can be combined with suitable payment functions so to obtain equilibria-truthful mechanisms achieving the same approximation ratio.... ..."

### Table 1: Approximation algorithms in this paper.

2003

"... In PAGE 4: ...Table 1: Approximation algorithms in this paper. Both the approximation factors and the time bounds depend on the properties of the regions and the set of orientations; the results are summarized in Table1 . More speci cally, in Section 4 we give a polynomial time approximation scheme (PTAS) when the graph is a tree.... ..."

Cited by 4

### Table 1. QoSMT problem with 2 rates. Runtime and approximation ratios of previ- ously known algorithms and of the algorithms given in this paper. In the runtime, n and m denote the number of nodes and edges in the original graph G = (V; E), respec- tively. Approximation ratios associated with polynomial-time approximation schemes are accompanied by a + to indicate that they approach the quoted value from above and do not reach this value in polynomial time.

2003

Cited by 5

### Table 1: Approximation ratios for scheduling with conflicts. The first two algorithms have running time exponential in m while the third has running time polynomial in m. Lines above the double rule refer to results based on previous work.

2007

"... In PAGE 4: ...3 Our results: the offline model. The approximation ratios in the offline model are summarized in Table1 . Given the hardness results mentioned previously, we focus on the basic case of m = 2.... ..."

### Table 2. Speedup in Worst-Case Execution Time for Optimized Virtual Table Algorithm

"... In PAGE 5: ... However, for the OVTA, the optimiza- tion over VTA depends completely on the characteristics of the generator polynomial chosen. Table2 shows the improvement over the VTA for several different polyno- mials (refer to Section 4 for a description of CRC32sub8 and CRC32sub16) . Note that for the particular CRC24 and CRC32 polynomials we used for our experiments, the OVTA has no improvement at all over the VTA.... ..."

### Table 1: Approximation ratios for scheduling with con icts. The rst two algorithms have running time exponential in m while the third has running time polynomial in m. Lines above the double rule refer to results based on previous work.

2007

"... In PAGE 4: ...3 Our results: the offline model. The approximation ratios in the of ine model are summarized in Table1 . Given the hardness results mentioned previously, we focus on the basic case of m = 2.... ..."

### Table 1 (continued)

"... In PAGE 5: ... We adopt the method for problem classiFFcation of Lageweg et al. [29] and present in Table1 the maximal easy problems (the most general cases of polynomially solvable problems) and the minimal hard problems (the most simple cases of NP problems). Other problems are cited below the table and are related to speciFFc problems described in the table.... ..."