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|
c the program is based on the paper u. derigs "solving non-bipartite
c matching problems via shortest path techniques" annals of operations
c research 7, 1988.
c Author :
c ulrich derigs
c lehrstuhl fur betriebswirtschaftslehre vii,
c universitat bayreuth, postfach 3008,
c d-8580 bayreuth, germany.
c ** *****************************************************************
subroutine prfmatch(n,m,np1,m2,nbl,cc,index,cost,nmatch,
+ basis,mem,ka,kb,sm,tma,tmb,y1,y2,dminus,dplus)
c *** (min-cost perfect matching problem) ***
integer basis(n),mem(n),ka(n),kb(n),sm(n),tma(n),tmb(n)
integer zfw,cost,nmatch(n),cc(m2),nbl(m2)
integer index(np1)
double precision y1(n),y2(n),dminus(n),dplus(n),eps
eps=10.**(-38)
sup=40000000
cost=400000000
do 1,i=1,n
nmatch(i)=0
1 continue
call sap(n,m,cc,nbl,index,zfw,nmatch,basis,mem,ka,kb,sm,
*tma,tmb,y1,y2,dplus,dminus,sup,eps)
cost=zfw
c zfw cost of the optimal matching
c nmatch(n) optimal matching
return
end
subroutine sap (n,m,cc,nbl,index,zfw,nmatch,basis,mem,ka,kb,
f sm,tma,tmb,y1,y2,dplus,dminus,sup,eps)
c ** *****************************************************************
c input:
c n number of nodes (even)
c m number of edges
c eps machine accuracy
c sup sufficiently large real number
c nbl(2*m) list of neighbours
c cc(2*m) cost of edges according to list of neighbours
c index(i) nbl(index(i)) start of neighbourlist of
c vertex i (i=1,..,n) with index(n+1)=2*m+1
c output:
c zfw cost of the optimal matching
c nmatch(n) optimal matching
c integer arrays of length n: basis,mem,ka,kb,sm,tma,tmb
c real*8 arrays of length n: y1,y2,dplus,dminus
c integer array of length n+1: index
c integer array of length 2*m: cc
c integer*2 array of length 2*m: nbl
c 5. external subroutines :
c augmnt expand grow ograph scan1 scan2 shrink start
c ** *****************************************************************
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
integer basis(1),mem(1),ka(1),kb(1),zfw,top,nmatch(1)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),c0,d,dbest,y1b,
* y2b,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** start
top =n+2
n2 =n/2
call start(n,ncard,top,cc,nbl,index,nmatch,y1)
if (ncard.eq.n2) goto 700
do 100 n1=1,n
basis(n1) =n1
mem(n1) =n1
y2(n1) =0.
sm(n1) =top
tma(n1) =top
tmb(n1) =top
dplus(n1) =sup
dminus(n1)=sup
ka(n1) =0
kb(n1) =n1
100 continue
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** initialization
nn =0
do 110 ni=1,n
if (nmatch(ni).ne.top) goto 110
nn =nn+1
sm(ni) =0
dplus(ni) =0.
110 continue
if (nn.le.1) goto 700
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** determination of the new dminus-values
120 do 140 n1=1,n
nb1 =basis(n1)
if (sm(nb1).ne.0) goto 140
y1b =y1(nb1)
y2b =y2(n1)
i1 =index(n1)
i2 =index(n1+1)-1
do 130 i3=i1,i2
n2 =nbl(i3)
nb2 =basis(n2)
if (nb1.eq.nb2) goto 130
nc =cc(i3)
c0 =dfloat(nc)-y1b-y2b
c0 =c0-y1(nb2)-y2(n2)
if (c0.ge.dminus(nb2)) goto 130
ka(nb2) =n1
kb(nb2) =n2
dminus(nb2)=c0
130 continue
140 continue
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** control-routine of the procedure
200 continue
dbest =sup
do 215 nb=1,n
if (basis(nb).ne.nb) goto 215
d =dminus(nb)
if (sm(nb).ge.top) goto 205
d =.5*(d+dplus(nb))
if (d.gt.dbest) goto 215
nbest =nb
dbest =d
g o t o 215
205 if (tma(nb).ge.top) goto 210
if (mem(nb).eq.nb) goto 215
d =d+y1(nb)
if (d.ge.dbest) goto 215
nbest =nb
dbest =d
g o t o 215
210 continue
if (d.ge.dbest) goto 215
nbest =nb
dbest =d
215 continue
if (tma(nbest).ge.top) goto 217
call bexpand(n,m,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest)
goto 200
217 if (sm (nbest).lt.top) goto 218
call grow(n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest)
goto 200
218 nka =ka(nbest)
nkb =kb(nbest)
n1 =nbest
nb1 =n1
n2 =basis(nka)
nb2 =n2
220 tma(nb1) =nb2
nk =sm(nb1)
if (nk.eq.0) goto 225
nb2 =basis(nk)
nb1 =tma(nb2)
nb1 =basis(nb1)
g o t o 220
225 nb =nb1
nb1 =n2
nb2 =n1
230 if (tma(nb1).lt.top) goto 235
tma(nb1) =nb2
nk =sm(nb1)
if (nk.ne.0) goto 232
call augmnt(n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,dbest,n1,n2,
f nka,nkb,ncard,j700)
if ( j700 .eq. 1 ) goto 700
goto 120
232 nb2 =basis(nk)
nb1 =tma(nb2)
nb1 =basis(nb1)
g o t o 230
235 if (nb1.ne.nb) goto 240
call shrink(n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest,
f nb,n1,n2,nb2,nka,nkb)
goto 200
240 nk =tma(nb)
tma(nb) =top
nm =nmatch(nk)
nb =basis(nm)
g o t o 235
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** generation of the original graph by expansion of all
c shrunken blossoms
700 call ograph(n,zfw,eps,index,nbl,cc,sm,tma,tmb,nmatch,mem,
f basis,ka,kb,dplus,dminus,y1,y2)
return
end
c************************************************************************
subroutine augmnt(n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,dbest,n1,n2,
f nka,nkb,ncard,jret1)
integer basis(1),mem(1),ka(1),kb(1)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer top,nmatch(1),nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),d,dbest,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** augmentation of the matching
c exchange of the matching- and non-matching-edges along the augmenting path
jret1 = 0
nb =n1
nk =nka
605 nb1 =nb
606 nmatch(nb1)=nk
nk =sm(nb1)
tma(nb1) =top
if (nk.eq.0) goto 607
nb2 =basis(nk)
nk1 =tma(nb2)
nk =tmb(nb2)
nb1 =basis(nk1)
nmatch(nb2)=nk1
g o t o 606
607 if (nb.ne.n1) goto 608
nb =n2
nk =nkb
g o t o 605
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** removing all labels on non-exposed base nodes
c
608 continue
do 620 nb=1,n
if (basis(nb).ne.nb) goto 620
if (sm(nb).ge.top) goto 610
d =dbest-dplus(nb)
y1(nb) =y1(nb)+d
sm(nb) =top
if (nmatch(nb).ne.top) goto 615
sm(nb) =0
dplus(nb) =0.
g o t o 616
610 if (tma(nb).ge.top) goto 615
d =dminus(nb)-dbest
y1(nb) =y1(nb)+d
tma(nb) =top
tmb(nb) =top
615 dplus(nb) =sup
616 dminus(nb)=sup
620 continue
ncard=ncard+1
ndiff=n-2*ncard
if(ndiff.gt.1) return
jret1=1
return
end
c*************************************************************************
subroutine bexpand(n,m,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest)
integer basis(1),mem(1),ka(1),kb(1)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer top,nmatch(1)
integer nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),dbest,y1b,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** expansion of a t-labeled blossom
c
500 continue
n1 =mem(nbest)
nb3 =n1
nka =ka(n1)
nk2 =n1
505 nk1 =nk2
nkb =kb(nk1)
y1b =y1(nk1)
510 basis(nk2)=nk1
y2(nk2) =y2(nk2)-y1b
if (nk2.eq.nkb) goto 515
nk2 =mem(nk2)
goto 510
515 nk2 =mem(nkb)
mem(nkb) =nk1
if (nk2.ne.nka) goto 505
y1b =dplus(n1)
y1(nbest) =y1b
mem(nbest)=nka
nk2 =nka
520 y2(nk2) =y2(nk2)-y1b
if (nk2.eq.nbest) goto 525
nk2 =mem(nk2)
goto 520
525 continue
nk1 =nmatch(nbest)
nb1 =basis(nk1)
nk2 =sm(nb1)
nb =basis(nk2)
if (nb.eq.nbest) goto 545
nb2 =nb
530 nk =tma(nb2)
nb1 =basis(nk)
if (nb1.eq.nbest) goto 535
nb2 =sm(nb1)
nb2 =basis(nb2)
goto 530
535 tma(nb) =tma(nbest)
tma(nbest)=tmb(nb2)
tmb(nb) =tmb(nbest)
tmb(nbest)=nk
nk3 =sm(nb)
nb3 =basis(nk3)
nk4 =sm(nb3)
sm(nb) =top
nmatch(nb)=nk1
nb1 =nb3
540 nk1 =tma(nb1)
nk2 =tmb(nb1)
tma(nb1) =nk4
tmb(nb1) =nk3
sm(nb1) =nk1
nmatch(nb1)=nk1
nb2 =basis(nk1)
nmatch(nb2)=nk2
nk3 =sm(nb2)
sm(nb2) =nk2
if (nb2.eq.nbest) goto 545
nb1 =basis(nk3)
nk4 =sm(nb1)
tma(nb2) =nk3
tmb(nb2) =nk4
goto 540
545 continue
nk2 =tmb(nb)
nb1 =basis(nk2)
dminus(nb1)=dbest
n1 =0
if (nb1.eq.nb) goto 555
nk1 =tma(nb1)
nb3 =basis(nk1)
tma(nb1) =tma(nb)
tmb(nb1) =nk2
550 nk =sm(nb1)
sm(nb1) =top
nb2 =basis(nk)
nk =tma(nb2)
tma(nb2) =top
n2 =tmb(nb2)
tmb(nb2) =n1
n1 =nb2
dplus(nb2)=dbest
nb1 =basis(nk)
dminus(nb1)=dbest
if (nb1.ne.nb) goto 550
tma(nb) =n2
tmb(nb) =nk
sm(nb) =top
if (nb3.eq.nb) goto 570
555 nb1 =0
nb2 =nb3
560 nk =sm(nb2)
sm(nb2) =top
tma(nb2) =top
tmb(nb2) =nb1
nb1 =basis(nk)
nk =tma(nb1)
sm(nb1) =top
tma(nb1) =top
tmb(nb1) =nb2
nb2 =basis(nk)
if (nb2.ne.nb) goto 560
call scan2(nb1,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
570 continue
575 if (n1.eq.0) return
nb =n1
call scan1(nb,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
n1 =tmb(nb)
tmb(nb) =top
g o t o 575
end
c***********************************************************************
subroutine grow (n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,y1,
f y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest)
c
integer basis(1),mem(1),ka(1),kb(1)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer top,nmatch(1)
integer nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),dbest,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** growing an alternating tree by adding two edges
c
tma(nbest)=ka(nbest)
tmb(nbest)=kb(nbest)
nm =nmatch(nbest)
nmb =basis(nm)
dplus(nmb)=dbest
sm(nmb) =nmatch(nmb)
call scan1(nmb,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
return
end
c***********************************************************************
subroutine ograph(n,zfw,eps,index,nbl,cc,sm,tma,tmb,nmatch,mem,
1 basis,ka,kb,dplus,dminus,y1,y2)
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
integer index(1),cc(1),sm(1),tma(1),tmb(1),n,zfw,
f nmatch(1),mem(1),basis(1),ka(1),kb(1)
integer nbl(1)
double precision dplus(1),dminus(1),y1(1),y2(1),d,yb,
f y1b,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** generation of the original graph by expansion of all
c shrunken blossoms
c
zfw =0
do 702 nb1=1,n
if (basis(nb1).ne.nb1) goto 702
if (sm(nb1).lt.0) goto 702
n2 =nmatch(nb1)
nb2 =basis(n2)
n1 =nmatch(nb2)
sm(nb1) =-1
sm(nb2) =-1
i1 =index(n1)
i2 =index(n1+1)-1
do 9000 i3=i1,i2
if(nbl(i3).eq.n2) go to 9001
9000 continue
9001 nc =cc(i3)
d =dfloat(nc)-y1(nb1)-y1(nb2)
d =d-y2(n1)-y2(n2)
if (dabs(d).gt.eps) continue
c see n1,n2,d
zfw =zfw+nc
702 continue
do 750 n1=1,n
705 nb =basis(n1)
if (nb.eq.n1) goto 750
nk2 =mem(nb)
nka =ka(nk2)
nb3 =nk2
yb =dplus(nk2)
710 nk1 =nk2
nkb =kb(nk1)
y1b =y1(nk1)
715 basis(nk2)=nk1
y2(nk2) =y2(nk2)-y1b
if (nk2.eq.nkb) goto 720
nk2 =mem(nk2)
goto 715
720 nk2 =mem(nkb)
mem(nkb) =nk1
if (nk2.ne.nka) goto 710
y1(nb) =yb
mem(nb) =nka
nk2 =nka
725 y2(nk2) =y2(nk2)-yb
if (nk2.eq.nb) goto 730
nk2 =mem(nk2)
goto 725
730 nk =nmatch(nb)
nk1 =basis(nk)
nk1 =nmatch(nk1)
nb1 =basis(nk1)
if (nb.eq.nb1) goto 745
nmatch(nb1)=nk
nb3 =tma(nb1)
nb3 =basis(nb3)
735 nk3 =sm(nb1)
nb2 =basis(nk3)
nk1 =tma(nb2)
nk2 =tmb(nb2)
nb1 =basis(nk1)
nmatch(nb1)=nk2
nmatch(nb2)=nk1
i1 =index(nk1)
i2 =index(nk1+1)-1
do 9002 i3=i1,i2
if(nbl(i3).eq.nk2) go to 9003
9002 continue
9003 nc =cc(i3)
d =dfloat(nc)-y1(nb1)-y1(nb2)
d =d-y2(nk1)-y2(nk2)
if (dabs(d).gt.eps) continue
c see nk1,nk2,d
zfw =zfw+nc
if (nb1.ne.nb) goto 735
740 if (nb3.eq.nb) goto 705
745 n2 =sm(nb3)
nb2 =basis(n2)
n3 =sm(nb2)
i1 =index(n2)
i2 =index(n2+1)-1
do 9004 i3=i1,i2
if(nbl(i3).eq.n3) go to 9005
9004 continue
9005 nc =cc(i3)
d =dfloat(nc)-y1(nb2)-y1(nb3)
d =d-y2(n2)-y2(n3)
if (dabs(d).gt.eps) continue
c see n2,n3,d
zfw =zfw+nc
n3 =tma(nb2)
nb3 =basis(n3)
goto 740
750 continue
return
end
c************************************************************************
subroutine scan1(nb1,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
integer n,top,basis(n),mem(n),ka(n),kb(n)
integer cc(1),sm(1),tma(1),tmb(1),index(1), nbl(1)
double precision y1(1),y2(1),dplus(1),dminus(1),d1,d2,c0
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** scanning of node nb1
top =n+2
d1 =dplus(nb1)-y1(nb1)
dminus(nb1)=sup
d2 =d1-y2(nb1)
tma(nb1) =0
ia =index(nb1)
ib =index(nb1+1)-1
do 300 ic=ia,ib
n2 =nbl(ic)
nb2 =basis(n2)
if (tma(nb2).lt.top) goto 300
nc =cc(ic)
c0 =dfloat(nc)+d2
c0 =c0-y1(nb2)-y2(n2)
if (c0.ge.dminus(nb2)) goto 300
ka(nb2) =nb1
kb(nb2) =n2
dminus(nb2)=c0
300 continue
n1 =nb1
g o t o 315
305 d2 =d1-y2(n1)
i1 =index(n1)
i2 =index(n1+1)-1
do 310 i3=i1,i2
n2 =nbl(i3)
nb2 =basis(n2)
if (tma(nb2).lt.top) go to 310
nc =cc(i3)
c0 =dfloat(nc)+d2
c0 =c0-y1(nb2)-y2(n2)
if (c0.ge.dminus(nb2)) goto 310
ka(nb2) =n1
kb(nb2) =n2
dminus(nb2)=c0
310 continue
315 n1 =mem(n1)
if (n1.ne.nb1) goto 305
tma(nb1) =top
return
end
subroutine scan2(nb,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
integer n,top
integer basis(n),mem(n),ka(n),kb(n)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),d,c0,y1b,
f y2b
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** scanning of node nb
c
top =n+2
300 nb1 =nb
nb =tmb(nb1)
tmb(nb1) =top
d =sup
nka =0
nkb =0
n1 =nb1
y1b =y1(nb1)
315 continue
y2b =y2(n1)
i1 =index(n1)
i2 =index(n1+1)-1
do 320 i3=i1,i2
n2 =nbl(i3)
nb2 =basis(n2)
if (sm(nb2).ge.top) goto 320
nc =cc(i3)
c0 =dfloat(nc)-y1b-y2b
c0 =c0-y1(nb2)-y2(n2)
c0 =c0+dplus(nb2)
if (c0.ge.d) goto 320
nka =n2
nkb =n1
d =c0
320 continue
n1 =mem(n1)
if (n1.ne.nb1) goto 315
ka(nb1) =nka
kb(nb1) =nkb
dminus(nb1)=d
if (nb.ne.0) goto 300
return
end
c***********************************************************************
subroutine shrink (n,top,nmatch,cc,basis,mem,ka,kb,sm,tma,tmb,
f y1,y2,dplus,dminus,sup,eps,nbl,index,nbest,dbest,
f nb,n1,n2,nb2,nka,nkb)
integer basis(1),mem(1),ka(1),kb(1)
integer cc(1),sm(1),tma(1),tmb(1),index(1)
integer top,nmatch(1)
integer nbl(1)
double precision y1(1),y2(1),dminus(1),dplus(1),dbest,y1b,
f yb,eps
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c *** shrinking a blossom
c
400 continue
yb =y1(nb)+dbest-dplus(nb)
y1(nb) =0.
nk1 =nb
430 y2(nk1) =y2(nk1)+yb
nk1 =mem(nk1)
if (nk1.ne.nb) goto 430
nk =mem(nb)
if (nb.ne.n2) goto 436
435 n2 =n1
nb2 =tma(nb)
436 mem(nk1) =nb2
nm =nmatch(nb2)
sm(nb2) =nm
y1b =y1(nb2)+dminus(nb2)-dbest
nk1 =nb2
440 nk2 =nk1
y2(nk2) =y2(nk2)+y1b
basis(nk2)=nb
nk1 =mem(nk2)
if (nk1.ne.nb2) goto 440
kb(nb2) =nk2
y1(nb2) =y1b
nb1 =basis(nm)
mem(nk2) =nb1
y1b =y1(nb1)+dbest-dplus(nb1)
nk2 =nb1
445 nk1 =nk2
y2(nk1) =y2(nk1)+y1b
basis(nk1)=nb
nk2 =mem(nk1)
if (nk2.ne.nb1) goto 445
kb(nb1) =nk1
y1(nb1) =y1b
if (n2.eq.nb1) goto 450
nb2 =tma(nb1)
tma(nb1) =tmb(nb2)
tmb(nb1) =tma(nb2)
goto 436
450 if (n2.eq.nbest) goto 455
tma(n2) =nkb
tmb(n2) =nka
if (nb.ne.nbest) goto 435
goto 460
455 tma(nbest)=nka
tmb(nbest)=nkb
460 mem(nk1) =nk
n1 =mem(nb)
ka(n1) =nk
dplus(n1) =yb
tma(nb) =top
dplus(nb) =dbest
call scan1(nb,n,sup,cc,basis,mem,ka,kb,sm,tma,tmb,
* y1,y2,dplus,dminus,nbl,index)
return
end
subroutine start(n,ncard,top,ce,nb,index,nmatch,y1)
c *** ****************************************************************
c * determination of an initial partial matching and a dual *
c * solution for starting the shortest augmenting path code *
c *** ****************************************************************
c * 1. call: *
c * call start(n,ncard,top,ce,nb,index,nmatch,y1) *
c * 3. method: *
c * - 1-saturated matching via greedy *
c * 4. parameters: *
c * input: *
c * n number of nodes *
c * top = n+2 *
c * nb(.) list of neighbours *
c * ce(.) costs of edges according to list of *
c * neighbours *
c * index(i) nb(index(i)) first neighbour of *
c * vertex i *
c * index(n+1) = n*(n-1)+1 ( for complete graphs ) *
c * output: *
c * nmatch(.) initial partial matching *
c * y1(.) initial dual solution *
c * ncard cardinality of partial matching *
c * *
c * integer array of length n : *
c * nmatch *
c * *
c * real*8 array of length n : *
c * y1 *
c * *
c * integer array of length n+1 : *
c * index *
c * *
c * integer*2 array of length n*(n-1) : *
c * nb *
c * *
c * integer array of length n*(n-1) : *
c * ce *
c *** ****************************************************************
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
integer ce(1),cq,index(1),nmatch(1),top
integer nb(1)
double precision d,dd,y1(1)
do 10 i=1,n
10 nmatch(i)=top
jjce=index(1)
cq=ce(jjce)
n1=index(n)-1
do 100 j=1,n1
if(cq.gt.ce(j)) cq=ce(j)
100 continue
d=dfloat(cq)/2.
do 110 i=1,n
110 y1(i)=d
ncard=0
do 150 i=1,n
if(nmatch(i).lt.top) goto 150
n1=0
n2=index(i)
n3=index(i+1)-1
jjnb=nb(n2)
d=dfloat(ce(n2))-y1(jjnb)
do 130 ik=n2,n3
j=nb(ik)
dd=dfloat(ce(ik))-y1(j)
if(dd.ge.d) goto 120
n1=j
d=dd
goto 130
120 if(dd.gt.d) goto 130
if(nmatch(j).lt.top) goto 130
n1=j
130 continue
if(n1.eq.0) goto 140
if(nmatch(n1).lt.top) goto 140
nmatch(i) =n1
nmatch(n1)=i
ncard=ncard+1
140 y1(i)=d
150 continue
return
end
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