### Table 4: Lower bounds using comb inequalities.

2004

"... In PAGE 12: ... For each such handle, we apply the above-mentioned procedure in an attempt to find a violated strengthened comb inequality. With this separation procedure, together with the separation of RCIs, we obtain the results displayed in Table4 . We find that the strengthened comb inequalities give an improvement over the bounds obtained by RCIs on eight instances.... ..."

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### Table 5: Lower bounds using multistar inequalities.

2004

"... In PAGE 13: ... For related results see [1, 12, 30]. Using our separation procedure for multistar (and partial multistar) in- equalities, together with the separation of RCIs, we obtain the results dis- played in Table5 . We find that the multistar inequalities give an improve- ment over the bounds obtained by RCIs on ten instances.... ..."

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### Table 6: Lower bounds using hypotour inequalities.

2004

"... In PAGE 16: ... In terms of computational complexity, the advantage of our procedure is that we avoid a complete path enumeration scheme, which may lead to excessive computing times unless accompanied by certain stopping criteria, as in [7, 12]. Using our separation procedure for 2EHs, together with the separation of RCIs, we obtain the results displayed in Table6 , which also displays the results obtained in [7, 12]. Our results are obtained after 25 calls to hypotour separation, after which the bounds increase only very little.... In PAGE 16: ... Our results are obtained after 25 calls to hypotour separation, after which the bounds increase only very little. None of the three sets of results in Table6 dominates the two others. We conclude that our procedure gives... ..."

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### Table 7. Lower bounds on ICE small for classes of valid inequalities

2004

"... In PAGE 20: ... In any of these runs, we held up to 1000 valid inequalities in the pool, in every iteration up to 100 inequalities could have been added, and after every iteration, weak cuts were deleted, if the cutting plane pool was full. Table7 presents average and extremal values for the lower bounds of the re- ned LP relaxations, when only one type of cuts has been added. Notice that we only add cycle inequalities in their original formulation (10) to strictly fundamental cycle bases.... ..."

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### Table 8. Lower bounds on ICE small for combinations of classes of inequalities

2004

"... In PAGE 21: ... Hence, roughly speaking, the headstart of short cycle bases is kept when adding change cycle inequali- ties. In Table8 , we consider combinations of types of valid inequalities to be added. One can observe that the best lower bounds were achieved, when at Table 8.... ..."

Cited by 2

### Table 1. Lower Bounds for Performance Metrics [7]

2004

Cited by 5

### Table 2: Lower bounds for metric space problems

### Table 1 shows that the HTER (i.e., TER with one human-targeted reference) reduces the edit rate by 33% relative to TER with 4 untargeted NIST references. Substitutions were reduced by the largest factor. In both TER and HTER, the majority of the edits were substitutions and deletions. Because TER is an edit-distance metric, lower numbers indicate better performance. In previous pilot studies with more experienced annotators, HTER yielded an even higher reduction of 50%.3

2006

"... In PAGE 7: ... Table1 : Untargeted (TER) and Human-targeted (HTER) Results: Average of S1 and S2 In an analysis of shift size and distance, we found that most shifts are short in length (1 word) and most shifts are by less than 7 words. We also did a side-by-side comparison of HTER with BLEU and METEOR (see Table 2),4 and found that human-targeted references lower edit distance overall but the TER measure is aided more than BLEU by targeted references: HTER yields a reduction of 33% whereas HBLEU yields a reduction of 28%.... ..."

Cited by 7

### Table 3: Parsing F -score of various feature and edit- detector combinations.

"... In PAGE 6: ... This metric is based on the assumption that there is little reason to recover syn- tactic structure in regions of speech that have been repaired or restarted by the speaker. Table3 shows the F -scores for the top-ranked parses after reranking, where the first-stage PCFG parser was run with a beam-size of 50. The first and last rows show lower and upper bounds, respec- tively, for reranked parsing accuracy on each edit condition.... ..."

### Table A.3: The E ect of Valid Inequalities on Percentage of Useful Lower Bound Esti- mates

1999

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