### Table 1. Comparison of performance for the sliding- window protocol

"... In PAGE 13: ... In contrast, QBDDs and their associated algorithms were designed to concisely represent the contents of queues and to e ciently compute queue operations. Table1 reports results of experiments performed with a more complex example of protocol: the full-duplex sliding-window protocol described in pages 232{233 of [30]. This protocol is modeled in about 100 lines of code in the input guarded command language for our tool.... In PAGE 14: ... The purpose of the protocol is to ensure that messages sent from the upper layer of one side are delivered in the same order to the upper layer of the other side. The results reported in Table1 were obtained with a domain of sequence numbers (used to number messages) of size 4 and with sliding-windows of size 2. These results show that QBDDs outperform BDDs again, both in time and memory, although the di erence in performance is less impressive, due to the use of smaller values for QSZ.... ..."

### Table 4: Optimal portfolios (VARs include 4 lags, constant, time trend, and quarterly seasonals)

"... In PAGE 32: ... From these observations, we see that it is no surprise why the estimated optimal debt portfolio is what it is. Next, turn to Table4 . This shows the results for a range of empirical speci - cations.... In PAGE 32: ... However, studying the values of the lagrange multipliers here (not displayed) shows that in each instance the omission of the other index-linked instruments is marginal|a slight perturbation would have brought other index-linked gilts into the optimal portfolio. Summarizing, Table4 warns us not to put too much weight on the speci cs of the optimal portfolio previously discussed (surrounding Table 3). It does con rm, however, that index-linked gilts should be favoured, and conventionals eschewed.... ..."

### Table 1. Average cycle length remains constant for random databases. This makes the stack search a constant time operation.

"... In PAGE 12: ... 1. The portion of the stack that needs to be searched for cycle detection is small because the average cycle length (see Table1 ) is small and remains constant. This makes the stack search operation effectively a35a37a36 a65a46a44 .... ..."

### Table 7: Results for the BNET-based implementation Implementation based on Logic Networks Derive LP F s (secs) Derive GPFs (secs) Total

"... In PAGE 24: ... In contrast, the substitution operation is very efficient (constant-time) under both BEDs and BNETs frameworks. Table7 lists the results obtained under the BNET scheme. Columns 2-3 list the CPU time spent (secs) to generate and optimize the LP F s of the propagation functions.... In PAGE 24: ... In our experiments, optimization is activated after 250MBs of memory has been used. Columns 5,6 and 7 of Table7 list the creation, optimization, and total time required to derive the GP F s of the propagation functions from the LP F s, respectively. The overall CPU time required by the BNET-based implementation is listed in Column 8.... In PAGE 27: ...8 of Table7 with Column 4 of Table 8). The major reason behind this speed-up is attributed to the reduction property of the BEDs.... ..."

### Table 1 indicates the general behavior of SPECjbb2000 in the two versions we measured: with one ware- house (single-threaded), and with four warehouses (multi-threaded). The minimum heap size is the experimentally determined smallest heap in which the program can run. The number of garbage collections needed by the semispace collector provides a crude measure of the load placed by the application on the collector. The maximum heap size used in our experiments is chosen so that the semispace collector needs at least 10 collections. Because the benchmark runs for a constant time, the amount of useful work varies depending on the efficiency of the collector, and thus the total amount allocated varies as well.

2005

"... In PAGE 7: ... Table1 : Benchmark information including the number of garbage collections performed by the semispace collector. 3.... ..."

### Table 2 reports the results for optimal L( 1; 2; : : : ; ?1)- coloring, known up to now in the literature. Speci cally, such a table indicates, for the most common regular net- works, the minimum number of channels required by a suf- ciently large network. In all the cases, there are e cient algorithms to assign channels to vertices. The channel as- signed to any vertex can be computed locally provided that the relative position of the vertex in the network is known. Such a computation can be performed in constant time for all the networks, except for binary trees which require log- arithmic time in the number of vertices. In particular, the

in Efficient Use of Radio Spectrum in Wireless Networks with Channel Separation between Close Stations

2000

"... In PAGE 9: ...L(1) L(0; 1) L(1; 1) L(2; 1) L(1; 1; 1) L(2; 1; 1) bus 2 2 3 5 4 5 ring 2 or 3 2 or 3 3 or 4 5 4 or 5 5 complete binary tree 2 3 4 5 6 7 hexagonal grid 2 3 4 6 6 7 bidimensional grid 2 4 5 7 8 9 cellular grid 3 6 7 9 12 12 References folklore [2, 10] [1, 3] [5, 7], this paper [3] this paper Table2 : Minimum number (G) + 1 of channels used for a su ciently large network G. on the grid, W[k] = 2 means that it is proceeding north- wards, while W[k] = 1 means that it is crossing a horizontal edge.... In PAGE 10: ... The proposed results extend those al- ready known in the literature for the L(0; 1)-, L(1; 1)- and L(1; 1; 1)-coloring problems. For the sake of completeness, Table2 reports also the minimum number of colors required by the L(1)-coloring problem, which reduces to the clas- sical minimum vertex coloring of a graph. From a the- oretical point of view, it remains as an open question to solve the general L( 1; 2; : : : ; ?1)-coloring problem, with 1 2 : : : ?1.... ..."

Cited by 16

### Table 2: Performance of the algorithm on di erent sliding window protocols

1996

"... In PAGE 21: ... Notice that if MaxSeq = 2, the sliding window protocol described above reduces to the Alternating Bit Protocol (Figure 1), and the speci cation reduces to that described in Figure 2. Table2 illustrates the performance of a draft implementation of the algo- rithm in the language C for di erent values of MaxSeq. The second column shows the number of control states in the product of the lossy channel system describing the protocol and the nite automaton representing the speci ca- tion.... In PAGE 21: ... As described in [Kin93], the veri cation time is dependent on the data structures used for the implementation of the sets W and V in the reachability algorithm (see Figure 3). Table2 describes the results of an implementation where the set W is implemented as a queue and the set V is implemented as a hash table. 7 Conclusion In this paper, we have shown that several types of safety and liveness prop- erties of systems of nite-state processes that communicate over unbounded but lossy FIFO channels are decidable.... ..."

Cited by 132

### Table 2. 4-width Sliding Window Method with NAF

2002

"... In PAGE 4: ...Table 2. 4-width Sliding Window Method with NAF The w-width sliding window method with NAF also use a pre-computed ta- ble (See Table2 ). As the optimal window size of this method (in the sense of efficiency) for 160-bit scalar multiplications is w = 4 [dWMPW98], we assume w = 4.... In PAGE 5: ... Denote ECDBLk by the k-time iteration of ECDBL. In Table2 we show the 4-width sliding window with NAF. In the pre-computation step, we compute 4 ECDBLs and 4 ECADDs.... ..."

Cited by 4

### Table 5: Memory footprints and runtimes for MSExplicit ver- sus Lea.

"... In PAGE 7: ... We do not yet have an explanatory model, but conjecture that this behav- ior arises because the survival rate from nursery collections is also inversely proportional to heap size. Finally, Table5 compares the footprints and runtimes of MSEx- plicit (explicit memory management based on the MMTk Mark- Sweep implementation) to the Lea allocator. MSExplicit is sub- stantially less memory-efficient than Lea, requiring on average 38%... ..."