Assignment and Matching Problems: Solution Methods with - download pdf or read online

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

ISBN-10: 3540102671

ISBN-13: 9783540102670

ISBN-10: 3642515762

ISBN-13: 9783642515767

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LJ The program requires a storage capacity of ~N2 + 13N. <:::! 3 sec Remarks: 1) In the SMP-code FLOATING-operations are used. Par several FORTRAN-compilers these operations are not needed and may be omitted. 2) In sorne application the storage capacity may be sufficiently large to handle the complete matrix. With respect to running time it is then favourable to store the cast matrix on an array C(I,J) with C(I,I) = SUP, (1,J = 1, ... ,N). In this case the pointer P(1) is not needed and the index-identification routines are replaced by the single statement Ne = C(I,J).

For R E Jt. we def ine y(R) the set of all edges with both ends in R. Then the linear description of SMP runs as follows: min r subject to x .. 1) eijEE (4. 2) X .. 1) for all R E J1. 3) for all e .. E E 1) SMP is equivalent to the SO called symmetrie assignment problem (SLSAP) . A permutation ~ E ~n is called symmetrie if

1. We will denote this operation by M1 =: :'19 P. Let ~~ be the set cf all augmenting paths with respect to M. Wltn every P E 1PM we can associate a length An augmenting path Po E 7P M is called shoY'tes t augmenting path with respect to M if for all P E Starting with the matching Mo = ~ 7PM • the SMP algorithm proceeds augrnen- ting along shartest augmenting paths only. Shortest augmenting path algorithm for sOlving SMP Iil (0) M = (1) IfMEJi (2) Determine Po E ~M with c (Po) (3) STOP, P 2 c (P) M is optimal!

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


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