### Table 1: Competitive ratio of L-greedy

"... In PAGE 4: ... For many such systems including net- worked reprographic machines, a theoretical model which does not incorporate lookahead runs the risk of being inapplicable to the real problem. More speci cally, we derive fairly tight results on the L-greedy, a natural greedy algo- rithm with lookahead L ( Table1 ). The term ML-greedy represents the competitive ratio of L-greedy with respect to the makespan performance metric which we de ne formally in Section 1.... ..."

### Table III presents an example to illustrate the performance metric of competitive ratio. Suppose all other TMs have CR(f; ftmg) less than 1.5. Then, maxtm2TM CR(f; ftmg), or oblivious ratio, is 1.5. Table III also shows that for some TM, the performance ratio can be lower than 1.5, e.g., for TM3, the ratio is 1.2. This shows that the oblivious routing f can performance better than the oblivious ratio predicts.

2006

Cited by 1

### Table 1: Lower bounds on the competitive ratio of on-line algorithms, depending on the platform type and on the objective function.

2005

"... In PAGE 5: ...erformance ratio will be, say, 1.1 while in another one (task T on P3) it will be, say, 1.2. Clearly, the minimum of the performance ratios over all execution scenarios is the desired bound on the competitive ratio of the algorithm: no algorithm can do better than this bound! Because we have three platform types (communication-homogeneous, computation-homoge- neous, fully heterogeneous) and three objective functions (makespan, max-flow, sum-flow), we have nine bounds to establish. Table1 summarizes the results, and shows the influence on the platform type on the difficulty of the problem. As expected, mixing both sources of heterogeneity (i.... In PAGE 20: ... We enforce the one-port model, and we study the impact of heterogeneity on the performance of scheduling algorithms. The major contribution of this paper lies on the theoretical side, and is well summarized by Table1 . We have provided a comprehensive set of lower bounds for the competitive ratio of any deterministic scheduling algorithm, for each source of heterogeneity and for each target objective function.... ..."

### Table 1: Lower bounds on the competitive ratio of on-line algorithms, depending on the platform type and on the objective function.

in The`me NUM

"... In PAGE 6: ....1 while in another one (task T on P3) it will be, say, 1.2. Clearly, the minimum of the performance ratios over all execution scenarios is the desired bound on the competitive ratio of the algorithm: no algorithm can do better than this bound! Because we have three platform types (communication-homogeneous, computation-ho- mogeneous, fully heterogeneous) and three objective functions (makespan, max-flow, sum- flow), we have nine bounds to establish. Table1 summarizes the results, and shows the influence on the platform type on the difficulty of the problem. As expected, mixing both sources of heterogeneity (i.... In PAGE 26: ... We enforce the one-port model, and we study the impact of heterogeneity on the performance of scheduling algorithms. The major contribution of this paper lies on the theoretical side, and is well summarized by Table1 . We have provided a comprehensive set of lower bounds for the competitive ratio of any deterministic scheduling algorithm, for each source of heterogeneity and for each target objective function.... ..."

### Table 1. Greedy competitive ratio (general cost)

"... In PAGE 4: ... The first set of our results deals with the competitive ratio of the Greedy Policy with regards to the global QoS metric, that is the sum of the costs of all the dis- carded frames under a well-behaved cost function. Our main result is presented in Table1 : for any sequence of frames, the competitive ratio of the Greedy Policy is... ..."

### Table 1 Best competitive ratios for UNIFORM

1992

"... In PAGE 6: ...his completes the proof of Theorem 3.1. Given a value of D, we can choose k to minimize the maximum of 1 + k+1 2D and 1 + 1 k ?2D + k+12 . Table1 shows the best competitive ratio for UNIFORM for values of D up to 10. These values are found by setting 1 + k + 1 2D = 1 + 1 k 2D + k + 1 2 and solving for k in terms of D.... ..."

Cited by 26

### Table 1: Bounds on the competitive ratio x implied

1995

"... In PAGE 8: ... 2 To get more detailed information on the best bound on x implied by #286#29, we consider the corresponding recurrence x = cp + p #20 p,1 lnc +1 x ! p,1 ; #287#29 for all c#3E1. Table1 shows the bounds on the com- petitive ratio x implied by #286#29, where the choice of c is optimized for each p. As p gets larger, the optimal value of c for use in #287#29 converges to the solution of the equation c ln c = 1, whichisc#191:77.... ..."

Cited by 22

### TABLE 1. Competitive ratios for the problems OLTRP and OLLDARP.

2001

Cited by 11

### TABLE 1. Competitive ratios for the problems OLTRP and OLLDARP.

2001

Cited by 11

### TABLE I COMPETITIVE RATIOS OF GREEDY FORWARDING

2005

Cited by 8