### Table 1. Tight performance ratios for given k.

"... In PAGE 115: ...swap push C8 BECZBV D1CPDC BG BF BG BF BK BJ C8 CZBV D1CPDC BE A0 BE D1B7BD BE A0 BE D1B7BD UB = BE A0 BE D1B7BD LB = BGD1 BFD1B7BD C9BECZBV D1CPDC BDB7 D4 BH BE BDB7 D4 BH BE D4 BDBJB7BD BG C9CZBV D1CPDC BDB7 D4 BGD1A0BF BE BDB7 D4 BGD1A0BF BE UB = BE A0 BE D1B7BD LB = BF BE A0 AF CABECZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D2 A0 BD undefined CACZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D4 D1CPDC A0BD C7C8CC undefined Table1 : performance guarantees: BV C4CB D1CPDC BPC7C8 CC same machine, then the swap neighborhood is empty; therefore, we define the swap neighborhood as one that consists of all possible jumps and all possible swaps. As can be seen in Table 1, the jump and swap neighborhoods have no constant performance guarantee for C9CZBV D1CPDC .... In PAGE 115: ...swap push C8 BECZBV D1CPDC BG BF BG BF BK BJ C8 CZBV D1CPDC BE A0 BE D1B7BD BE A0 BE D1B7BD UB = BE A0 BE D1B7BD LB = BGD1 BFD1B7BD C9BECZBV D1CPDC BDB7 D4 BH BE BDB7 D4 BH BE D4 BDBJB7BD BG C9CZBV D1CPDC BDB7 D4 BGD1A0BF BE BDB7 D4 BGD1A0BF BE UB = BE A0 BE D1B7BD LB = BF BE A0 AF CABECZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D2 A0 BD undefined CACZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D4 D1CPDC A0BD C7C8CC undefined Table 1: performance guarantees: BV C4CB D1CPDC BPC7C8 CC same machine, then the swap neighborhood is empty; therefore, we define the swap neighborhood as one that consists of all possible jumps and all possible swaps. As can be seen in Table1 , the jump and swap neighborhoods have no constant performance guarantee for C9CZBV D1CPDC . Therefore, we introduce a push neighborhood, for which any local optimum is at most a factor BE A0 BE D1B7BD of optimal for C9CZBV D1CPDC .... In PAGE 115: ... When pushing all jobs on the critical machines is unsuccessful, we are in a push optimal solution. In Table1 the performance guarantees for the various local optima and scheduling problems are given. UB = AQ denotes that AQ is a performance guarantee and LB = AQ denotes that the performance guarantee cannot be less than AQ; AQ denotes that UB = LB = AQ.... In PAGE 121: ...Empty Out-tree To approximate solution 0,079 0,005 Tolower bound 0,115 0,318 Table1 : Average relative errors of approximate solution of algorithm based on y jt -formulation to approximate solution of algorithm based on x jt -formulation and lower bound ( = 1). The graph of precedence constraints Empty Out-tree To approximate solution 0,048 0,001 Tolower bound 0,073 0,309 Table 2: Average relative errors of approximate solution of algorithm based on y jt -formulation to approximate solution of algorithm based on x jt -formulation and lower bound ( =1= p 2).... ..."

### Table 6: Using DAG width as the RC size

"... In PAGE 8: ... In fact, the DAG width is an upper bound on the optimal RC size. Table6 presents results similar to those in Table 4 and Table 5, showing average performance and cost degradation from best, but obtained when using DAG width as the RC size. The first prominent numbers that provided stark contrast to the numbers for our prediction model are the relative costs.... ..."

### Table 3. The number of DAG

2003

"... In PAGE 5: ... Table 4 shows the performance of Optimal Reinsertion search against hill climbing. Table3 shows the number of structures searched by Optimal Reinsertion for each dataset. In most (but not all) cases Optimal Reinsertion quickly finds a better solution than Hill-climbing ever finds.... ..."

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### Table 3. The number of DAG

2003

"... In PAGE 5: ... Table 4 shows the performance of Optimal Reinsertion search against hill climbing. Table3 shows the number of structures searched by Optimal Reinsertion for each dataset. In most (but not all) cases Optimal Reinsertion quickly finds a better solution than Hill-climbing ever finds.... ..."

Cited by 23

### Table 1: Tight bounds on closeness of synchronization.

2001

Cited by 11

### Table 1: Tightness of Heuristic Register Bound

"... In PAGE 16: ... Notice that underestimations are often xed by the sequencing algorithm. All the results presented in Table1 (a) are for small DDGs with a low MRR for which the ILP method can nd a solution.... In PAGE 17: ...E ectiveness of Heuristic Methods in Larger DDGs How good is our heuristic solution for the 181 DDGs for which the ILP approach failed to nd an optimal solution? The rst column of Table1 (b) reports the number of DDGs for which an instruction sequence was found that used HRB registers. The table also shows the number of DDGs for which the instruction sequence requires more registers than HRB, the average register increase and the maximum register increase for each method.... ..."

### Table 1. Summary of complexity results (all bounds are tight)

2000

"... In PAGE 5: ... In the following, without loss of generality, we con- sider only the problem of checking whether a pair of objects is a certain answer of a query. 3 Summary of Results and Related Work The summary of our results on the complexity of an- swering regular path queries using views is reported in Table1 . Entries with all sound (resp.... ..."

Cited by 58