### Table 2, where row \1 quot; indicates the complexity of nding a tree spanner (with minimum weight if G is weighted). The complexity of quasitree spanner problems on weighted digraphs and unweighted digraphs is the same as that of tree spanner problems on weighted graphs and unweighted graphs respectively.

1995

"... In PAGE 37: ... Table2 : The complexity status of tree spanner problems Note that the tree 3-spanner problem on unweighted graphs and the quasitree 3-spanner problem on unweighted digraphs remain open. We conjecture that the tree 3-spanner problem on unweighted graphs is NP-complete; if true it would imply the NP-completeness of the quasitree 3-spanner problem on unweighted digraphs.... ..."

Cited by 47

### Table A.2: An example for minimum weight edge cover problem algorithm based on the Hungarian algorithm.

### Table 1: Errors minimum weight for a work factor greater than 280

### Table 8: Minimum weight values for the 10-bar truss shown in Figure 6 over 10 different runs Minimum Number of

"... In PAGE 36: ... The values a = b = 200000 are used for the parameters in Equation 9. The best solutions obtained for this truss and the number of solutions evaluated in a sequence of 10 runs with different random seeds in the proposed approach are given in Table8 . While the best solutions given by Rajeev and Krishnamoorthy [15] and Elperin [4] have a weight of 22653:55 Nand 25829:73 respectively, the proposed approach generates a solution with a weight of 22573:68 N.... In PAGE 80: ...Table 7: pj for optimal solution shown in Figure 6, when base is fixed and rreq =10 W-shape Members W14 193 1,2,11,12,21,22 31,32,41,42,51,52 W14 99 3,4,13,14,24 34,43,44,53,54 W14 120 23,33 W14 90 5,15,25,35,45,55 W12 22 6,16,36,46 W21 44 7,9,27,29,47,49 W21 55 8,18,28,38,48 W18 35 10,20,30,40,50 W18 40 17,37 W24 68 19,39 W16 31 26 Table8 : pj for optimal solution shown in Figure 7, when base is hinged and rreq =6 W-shape Members W14 211 1,11,21,31,41,51 W14 145 2,12,22,32,42,52 W14 90 3,13,23,33,43,53 W14 53 4,14,24,34,44,54 5,15,25,35,45,55 W12 14 6,16,36,46 W16 26 7,17,37,47 W21 48 8,18,28,38,48 10,20,40,50 W18 40 9,49 W21 44 19,39 W14 22 26 W33 118 29 W40 199 27,30 Table 9: Optimal cost for different values of Cr=Cs, when the base is fixed for 5-bay 5-story frame Cost of rigid Cost of steel Cost Ratio Least-weight Cost-optimal solution % reduction connection (Cr) per ton (Cs) (CR) design cost ($) rreq Cost ($) in total cost 750.00 750.... ..."

### Table 1: Assigning edge weights for the graph cuts problem. Notation is as enumerated in Section 4 and equations 2,3,4. This table is taken from [BJ01] and is mentioned here for completeness.

"... In PAGE 5: ...This is achieved by assigning appropriate weights to the edges of the graph and finding a minimum-weight edge cut of the graph such that the two special nodes are in sepa- rate components. The edge weights are assigned as enumer- ated in Table1 . Our algorithm performs segmentation in two passes: in the first pass it performs image segmentation us- ing GI and in the second pass it performs 3D segmentation by projecting the clusters created by the over-segmentation (Section 5).... ..."

### Table 5: AER[%] for different alignment symmetrization methods and for various alignment models on the Canadian Hansards and the Verbmobil tasks (MWEC: minimum weight edge cover, EW: empty word).

2004

"... In PAGE 6: ...Lines 2a and 2b of Table5 show the perfor- mance of the MWEC algorithm. The align- ment error rates are slightly lower if the HMM or the full Model 6 training scheme is used to train the state occupation probabilities on the Canadian Hansards task.... In PAGE 6: ...1%. Columns 4 and 5 of Table5 contain the re- sults of the experiments, in which the costs cij were determined as the loglinear interpola- tion of state occupation probabilities obtained from the HMM training scheme with those from IBM-4 (column 4) or from Model 6 (col- umn 5). We set the interpolation parameters for the two translation directions proportional to the optimal values determined in the previ- ous experiments.... In PAGE 6: ... In addition, we used a combination heuristic to obtain a symmetric alignment. The results of these experiments are presented in Table5 , lines 4-6 a/b. The performance of the one-sided MWEC algorithm turned out to be quite robust on both tasks.... In PAGE 6: ... That is why on the Verbmobil task, when determining the mininum weight in each row for the translation direction from En- glish to German, the alignment quality deteri- orates, because the algorithm cannot produce alignments which map several English words to one German word (line 5b of Table 5). Applying the generalization heuristics (line 6a/b of Table5 ), we achieve an AER of 6.0% on the Canadian Hansards task when interpolating the state occupation probabil- ities trained with the HMM and with the IBM-4 schemes.... ..."

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### Table 7: Minimum weight optimization problem for bladed-stiffened

1999

Cited by 1