### Table 3: Lower bounds and R1 A for various algorithms. idea to general . The proof in [42] was considerably simpli ed by Galambos and Frenk [43]. Van Vliet gave an exhaustive analysis of the lower bound constructions with a linear programming technique applied to all : his lower bound is the best so far. Theorem 3.17 (van Vliet [96]). For any on-line algorithm A, R1 A 1:540.

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"... In PAGE 31: ...heorem 3.17 (van Vliet [96]). For any on-line algorithm A, R1 A 1:540. Table3 gives a comparison for several values of = 1 r between the best lower bounds and the corresponding upper bounds for various algorithms. It is interesting to note that the gap between the lower and upper bounds becomes rather small for r 2.... ..."

### Table 4: An example demonstrating the idea of SHEI

"... In PAGE 25: ... By alternating the direction of sorting in successive keys, our algorithm can distribute the workload quite evenly, while maintaining a reasonably high skewness. This idea of using auxiliary sort keys and alternating sort orders is illustrated in Table4 . Here, the primary sort key is k1, while k2 is the secondary sort key.... ..."

### Table 1 Summary of admission control algorithms compared. Rate Envelope Multiplexing (REM) de- scribes the approach where the effect of buffering is not taken into account, while Rate-Sharing Multiplexing (RSM) takes into account gains made through buffering. Certainty Equivalence describes MBAC algorithms that are not robust to the random properties of measurements AC algorithm Key idea Buffering Certainty

"... In PAGE 3: ... Such an algorithm allows computation of the performance-frontierillustrated in Section 4 and described more fully therein. The above AC algorithms are summarised in Table1 along with the key idea behind each algorithm and several comparison criteria. Table 1 Summary of admission control algorithms compared.... In PAGE 4: ...W. Moore / An implementation-based comparison of Measurement-Based Admission Control algorithms Whether the gains made though buffering are taken into account by an AC is indicated by the column Buffer Effect of Table1 . The Rate Envelope Multiplexing (REM) approach does not take the effect of buffering into account, while Rate-Sharing Multiplexing (RSM) takes into account gains made through buffering.... In PAGE 4: ... For algorithms that are measurement-based the incorporation of an RSM approach may be implicit, such as that of AC-MS or explicit such as AC-KQ or AC-MPFE. Table1 also lists which of the MBAC algorithm are based upon Certainty Equivalence. Certainty Equivalence in AC algorithms is the use of a static AC algorithm but with the insertion of measurement derived estimations rather than those computed from aprioritraffic descriptors [28].... ..."

### Table 2. In this table, state-of-the-art document logical structure analysis algorithms are analyzed in terms of key idea, physical layout representation, logical structure representation, output representation, logical labels and application domain.

"... In PAGE 7: ... 5. SUMMARY AND LIMITATIONS OF THE SURVEYED ALGORITHMS Table2 summarizes the surveyed algorithms in terms of key idea, physical layout representation, logical structure representation, logical labels, output representation, and application domain. As pointed out in Section 2 and Section 3, most of the past work on document structure analysis has been limited in one or more respects: 1.... ..."

### Table 2. In this table, state-of-the-art document logical structure analysis algorithms are analyzed in terms of key idea, physical layout representation, logical structure representation, output representation, logical labels and application domain.

"... In PAGE 7: ... 5. SUMMARY AND LIMITATIONS OF THE SURVEYED ALGORITHMS Table2 summarizes the surveyed algorithms in terms of key idea, physical layout representation, logical structure representation, logical labels, output representation, and application domain. As pointed out in Section 2 and Section 3, most of the past work on document structure analysis has been limited in one or more respects: 1.... ..."

### (Table 2, step 2), then the customer submits the pay- ment to the trusted agent (step 3). The trusted agent may then notify the vendor and get the encryption key from the vendor (step 4). The exchange ends when the TA sends the encryption key to the customer and pay- ment to the vendor, as shown in step 5 and 6 respec- tively. Note that the deliveries of the encrypted goods and encryption key should be done in private. Any traditional symmetric-key algorithms such as DES and IDEA could be used for encryption.

1997

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### Table 3 gives a rough idea of the main features and differences existing

1986

"... In PAGE 18: ...MEMORY Yes No # NEIGHBORS 9 13 OP.MODE 1 SIMD 1 SIMD LANGUAGES ( PLANB 1 PPASCAL SPHINX GPIA NMOS NMOS 44 I 48 3 2 -i- No 16bits No 2 Yes No 67bits No 7 YeS Yes ~ 256bits Yes I 9 SIMD 1 SIMD No I PCL - - - Some remarks concerning Table3 are appropriate. PCLIP seems to have the best neighbor connection scheme, allowing easier and faster implementa- tions of algorithms requiring mainly local computation.... ..."

### Table 1 We are currently programming the GMRZ and also lling up the void places in Table 1. In particular, it will be interesting to derive the algorithm based on L anczos/Orthodir for treating near{breakdowns in the CGS, since this algorithm is the only reliable one for implementing L anczos method. The ideas developed in this paper only became clear after programming the algorithms and testing them on many numerical examples, which shows once more, if necessary, that, as stated by P. Wynn [56]

"... In PAGE 9: ... FORTRAN subroutines corresponding to some of these algorithms can be found in [15] together with numerical examples; see also [10, 16]. Let us mention that Gutknecht proposed an unnormalized version of the BIORES algorithm for curing ghost breakdowns in the BIORES by using a three{term recurrence relationship and, by squaring it, he obtained the unnormalized BIORES2 for treating ghost breakdowns in the CGS [30] (these algorithms will be respectively denoted by uBIORES and uBIORES2 in Table1 below). Another procedure for treating breakdowns in the classical L anczos algorithm is described in [4].... ..."

### Table 6.2: Log-log analysis of the run-times on noisy KRK data. In order to get an idea on the asymptotic complexity of the various algorithms we have performed a log-log analysis as has been done in [Cameron-Jones, 1994]. Dividing the logarithm of the run-time by the logarithm of the training set size 2As in the over tting phase only 2=3 of the training data are used for learning, the Initial Rule Growth column should only be used with caution for comparing pruning to non-pruning approaches, in particular with respect to the accuracy results. However, one could choose to compare e.g. the Initial Rule Growth results for 750 examples with the results of the pruning algorithms for 500 examples to get an idea how much improvement in terms of accuracy pruning brings in this domain.

### Table 1 Training set correctness using the unsupervised k-Median and k-Mean Algorithms and the supervised Robust LP on four databases Remark 3.2 Testing Set Correctness The idea behind this approach

1997

"... In PAGE 4: ... The k-Median training set correctness is compared to that of the k-Mean Algorithm as well as the training correctness of a supervised learning method, a perceptron trained by robust linear programming [2]. Table1... ..."

Cited by 47