By Rainer E. Burkard, Ulrich Derigs (auth.)

ISBN-10: 3540102671

ISBN-13: 9783540102670

ISBN-10: 3642515762

ISBN-13: 9783642515767

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**Extra resources for Assignment and Matching Problems: Solution Methods with FORTRAN-Programs**

**Sample text**

DERIGS G. O) GOTO 120 SM(I ) -0 STACK(IT) -I IT =IT+l CONTINUE IS -I 00 50 53 55 110 120 31 G C G *** GROWING ALTERNATING TREES FROM EACH UNSATURATEO VERTEX 200 GONTINUE =STACK(IS) NS -BASIS (NS) NBS TMA(NBS) =0 =INOEX(NS) I -NS+I II -INOEX(II )-1 II NI .. NK2) IZ =IZ+! , 10X, 15HNUMBER OF EDGES, 14) FORMAT(/! ,46RERROR: TRE VERTEX DEGREES DO NOT SUM UP TO 2*M) STOP END 35 CARDINALITY MATCHING PROBLEM NUMBER NUMB ER OF NODES NUMBER OF EDGES LI ST OF EDGES LIST 2 12 l2 3 15 l5 17 l7 19 19 24 27 4 6 8 5 4 5 5 6 6 6 6 7 8 10 lD 12 l2 13 l3 13 l3 14 l4 14 l4 14 l4 14 l4 1l 5 15 l5 l6 16 l8 18 18 l8 20 21 2l 21 2I 21 22 22 23 23 24 25 26 lO 10 6 9 7 8 9 lO 10 11 II 9 11 II 13 l3 l4 14 15 l5 16 l6 18 l8 20 21 2l l7 17 20 17 l7 2l 21 25 21 2l 22 23 25 23 25 24 26 27 26 27 27 46 36 OPTIMAL lIATCHING 1 12 2 3 4 S 6 19 8 10 9 0 8 9 10 3 S 4 12 13 1 15 7 11 11 7 14 20 15 16 17 18 13 17 16 21 19 20 2 14 21 18 22 23 24 2S 25 24 23 22 26 27 27 26 CARDINALITY OF TRE OPTIMAL MATCRING 13 10 11 26 Fig.

IN. 1,2, ... ,Nand + J Then we find the Cüst element C(I,J) as CC(IND). ) 44 OUTPUT: The main prograrn prints out the name of the problem and the cast matrix C = (C ij ). The optimal matching M is stored on the vector NMATCH(I) and is printed out in the form I - - 1= 1,2, ... ,N NMATCH (I) which means that the edge connecting land NMATCH(I) is a matehing edge. ~EM c ij of the optimal matching is given. lJ The program requires a storage capacity of ~N2 + 13N. <:::! 3 sec Remarks: 1) In the SMP-code FLOATING-operations are used.

C ji < c i i + c .. lj ]] + Cj j else for i,j E N , i*j . Now let M be the optimal solution for SMP. An optimal symmetrie assignrnent e .. E M .. l] ;p li) ;Pli) and =i ;p I j ) = (jJ Ein i can be obtained as follows: if cij+c Jl < cii+Cji else and ;Plj) b) Description cf the algorithrn The algorithm presented here is an adaption of the LSAP-algorithrn to the nonbipartite case. We assume G = (V,E) to be complete with IV\ even and the weigths c ij for e ij E E to be nonnegative integer/real nurnbers.

### Assignment and Matching Problems: Solution Methods with FORTRAN-Programs by Rainer E. Burkard, Ulrich Derigs (auth.)

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