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577 lines
20 KiB
Fortran
577 lines
20 KiB
Fortran
SUBROUTINE REDUCE(NDSTK, NR, IOLD, RENUM, NDEG, LVL, LVLS1,
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* LVLS2, CCSTOR, IBW2, IPF2)
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C SUBROUTINE REDUCE DETERMINES A ROW AND COLUMN PERMUTATION WHICH,
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C WHEN APPLIED TO A GIVEN SPARSE MATRIX, PRODUCES A PERMUTED
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C MATRIX WITH A SMALLER BANDWIDTH AND PROFILE.
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C THE INPUT ARRAY IS A CONNECTION TABLE WHICH REPRESENTS THE
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C INDICES OF THE NONZERO ELEMENTS OF THE MATRIX, A. THE ALGO-
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C RITHM IS DESCRIBED IN TERMS OF THE ADJACENCY GRAPH WHICH
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C HAS THE CHARACTERISTIC THAT THERE IS AN EDGE (CONNECTION)
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C BETWEEN NODES I AND J IF A(I,J) .NE. 0 AND I .NE. J.
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C DIMENSIONING INFORMATION--THE FOLLOWING INTEGER ARRAYS MUST BE
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C DIMENSIONED IN THE CALLING ROUTINE.
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C NDSTK(NR,D1) D1 IS .GE. MAXIMUM DEGREE OF ALL NODES.
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C IOLD(D2) D2 AND NR ARE .GE. THE TOTAL NUMBER OF
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C RENUM(D2+1) NODES IN THE GRAPH.
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C NDEG(D2) STORAGE REQUIREMENTS CAN BE SIGNIFICANTLY
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C LVL(D2) DECREASED FOR IBM 360 AND 370 COMPUTERS
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C LVLS1(D2) BY REPLACING INTEGER NDSTK BY
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C LVLS2(D2) INTEGER*2 NDSTK IN SUBROUTINES REDUCE,
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C CCSTOR(D2) DGREE, FNDIAM, TREE AND NUMBER.
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C COMMON INFORMATION--THE FOLLOWING COMMON BLOCK MUST BE IN THE
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C CALLING ROUTINE.
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C COMMON/GRA/N,IDPTH,IDEG
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C EXPLANATION OF INPUT VARIABLES--
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C NDSTK- CONNECTION TABLE REPRESENTING GRAPH.
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C NDSTK(I,J)=NODE NUMBER OF JTH CONNECTION TO NODE
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C NUMBER I. A CONNECTION OF A NODE TO ITSELF IS NOT
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C LISTED. EXTRA POSITIONS MUST HAVE ZERO FILL.
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C NR- ROW DIMENSION ASSIGNED NDSTK IN CALLING PROGRAM.
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C IOLD(I)- NUMBERING OF ITH NODE UPON INPUT.
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C IF NO NUMBERING EXISTS THEN IOLD(I)=I.
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C N- NUMBER OF NODES IN GRAPH (EQUAL TO ORDER OF MATRIX).
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C IDEG- MAXIMUM DEGREE OF ANY NODE IN THE GRAPH.
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C EXPLANATION OF OUTPUT VARIABLES--
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C RENUM(I)- THE NEW NUMBER FOR THE ITH NODE.
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C NDEG(I)- THE DEGREE OF THE ITH NODE.
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C IBW2- THE BANDWIDTH AFTER RENUMBERING.
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C IPF2- THE PROFILE AFTER RENUMBERING.
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C IDPTH- NUMBER OF LEVELS IN REDUCE LEVEL STRUCTURE.
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C THE FOLLOWING ONLY HAVE MEANING IF THE GRAPH WAS CONNECTED--
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C LVL(I)- INDEX INTO LVLS1 TO THE FIRST NODE IN LEVEL I.
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C LVL(I+1)-LVL(I)= NUMBER OF NODES IN ITH LEVEL
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C LVLS1- NODE NUMBERS LISTED BY LEVEL.
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C LVLS2(I)- THE LEVEL ASSIGNED TO NODE I BY REDUCE.
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C WORKING STORAGE VARIABLE--
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C CCSTOR
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C LOCAL STORAGE--
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C COMMON/CC/-SUBROUTINES REDUCE, SORT2 AND PIKLVL ASSUME THAT
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C THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
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C SUBROUTINE FNDIAM ASSUMES THAT THERE ARE AT MOST
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C 100 NODES IN THE LAST LEVEL.
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C COMMON/LVLW/-SUBROUTINES SETUP AND PIKLVL ASSUME THAT THERE
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C ARE AT MOST 100 LEVELS.
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C USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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INTEGER NDSTK
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INTEGER STNODE, RVNODE, RENUM, XC, SORT2, STNUM, CCSTOR,
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* SIZE, STPT, SBNUM
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COMMON /GRA/ N, IDPTH, IDEG
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C IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
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COMMON /CC/ XC, SIZE(5000), STPT(5000)
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COMMON /LVLW/ NHIGH(10000), NLOW(10000), NACUM(10000)
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save gra, cc, lvlw
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DIMENSION CCSTOR(1), IOLD(1)
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DIMENSION NDSTK(NR,1), LVL(1), LVLS1(1), LVLS2(1), RENUM(1),
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* NDEG(1)
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IBW2 = 0
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IPF2 = 0
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C SET RENUM(I)=0 FOR ALL I TO INDICATE NODE I IS UNNUMBERED
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DO 10 I=1,N
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RENUM(I) = 0
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10 CONTINUE
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C COMPUTE DEGREE OF EACH NODE AND ORIGINAL BANDWIDTH AND PROFILE
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CALL DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1)
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C SBNUM= LOW END OF AVAILABLE NUMBERS FOR RENUMBERING
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C STNUM= HIGH END OF AVAILABLE NUMBERS FOR RENUMBERING
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SBNUM = 1
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STNUM = N
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C NUMBER THE NODES OF DEGREE ZERO
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DO 20 I=1,N
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IF (NDEG(I).GT.0) GO TO 20
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RENUM(I) = STNUM
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STNUM = STNUM - 1
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20 CONTINUE
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C FIND AN UNNUMBERED NODE OF MIN DEGREE TO START ON
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30 LOWDG = IDEG + 1
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NFLG = 1
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ISDIR = 1
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DO 40 I=1,N
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IF (NDEG(I).GE.LOWDG) GO TO 40
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IF (RENUM(I).GT.0) GO TO 40
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LOWDG = NDEG(I)
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STNODE = I
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40 CONTINUE
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C FIND PSEUDO-DIAMETER AND ASSOCIATED LEVEL STRUCTURES.
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C STNODE AND RVNODE ARE THE ENDS OF THE DIAM AND LVLS1 AND LVLS2
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C ARE THE RESPECTIVE LEVEL STRUCTURES.
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CALL FNDIAM(STNODE, RVNODE, NDSTK, NR, NDEG, LVL, LVLS1,
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* LVLS2, CCSTOR, IDFLT)
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IF (NDEG(STNODE).LE.NDEG(RVNODE)) GO TO 50
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C NFLG INDICATES THE END TO BEGIN NUMBERING ON
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NFLG = -1
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STNODE = RVNODE
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50 CALL GPS_SETUP(LVL, LVLS1, LVLS2)
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C FIND ALL THE CONNECTED COMPONENTS (XC COUNTS THEM)
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XC = 0
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LROOT = 1
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LVLN = 1
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DO 60 I=1,N
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IF (LVL(I).NE.0) GO TO 60
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XC = XC + 1
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STPT(XC) = LROOT
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CALL TREE(I, NDSTK, NR, LVL, CCSTOR, NDEG, LVLWTH, LVLBOT,
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* LVLN, MAXLW, N)
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SIZE(XC) = LVLBOT + LVLWTH - LROOT
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LROOT = LVLBOT + LVLWTH
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LVLN = LROOT
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60 CONTINUE
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IF (SORT2(DMY).EQ.0) GO TO 70
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CALL PIKLVL(LVLS1, LVLS2, CCSTOR, IDFLT, ISDIR)
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C ON RETURN FROM PIKLVL, ISDIR INDICATES THE DIRECTION THE LARGEST
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C COMPONENT FELL. ISDIR IS MODIFIED NOW TO INDICATE THE NUMBERING
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C DIRECTION. NUM IS SET TO THE PROPER VALUE FOR THIS DIRECTION.
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70 ISDIR = ISDIR*NFLG
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NUM = SBNUM
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IF (ISDIR.LT.0) NUM = STNUM
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CALL NUMBER(STNODE, NUM, NDSTK, LVLS2, NDEG, RENUM, LVLS1,
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* LVL, NR, NFLG, IBW2, IPF2, CCSTOR, ISDIR)
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C UPDATE STNUM OR SBNUM AFTER NUMBERING
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IF (ISDIR.LT.0) STNUM = NUM
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IF (ISDIR.GT.0) SBNUM = NUM
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IF (SBNUM.LE.STNUM) GO TO 30
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IF (IBW2.LE.IBW1) RETURN
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C IF ORIGINAL NUMBERING IS BETTER THAN NEW ONE, SET UP TO RETURN IT
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DO 80 I=1,N
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RENUM(I) = IOLD(I)
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80 CONTINUE
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IBW2 = IBW1
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IPF2 = IPF1
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RETURN
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END
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SUBROUTINE DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1)
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C DGREE COMPUTES THE DEGREE OF EACH NODE IN NDSTK AND STORES
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C IT IN THE ARRAY NDEG. THE BANDWIDTH AND PROFILE FOR THE ORIGINAL
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C OR INPUT RENUMBERING OF THE GRAPH IS COMPUTED ALSO.
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C USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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INTEGER NDSTK
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COMMON /GRA/ N, IDPTH, IDEG
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DIMENSION NDSTK(NR,1), NDEG(1), IOLD(1)
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IBW1 = 0
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IPF1 = 0
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DO 40 I=1,N
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NDEG(I) = 0
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IRW = 0
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DO 20 J=1,IDEG
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ITST = NDSTK(I,J)
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IF (ITST) 30, 30, 10
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10 NDEG(I) = NDEG(I) + 1
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IDIF = IOLD(I) - IOLD(ITST)
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IF (IRW.LT.IDIF) IRW = IDIF
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20 CONTINUE
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30 IPF1 = IPF1 + IRW
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IF (IRW.GT.IBW1) IBW1 = IRW
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40 CONTINUE
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RETURN
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END
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SUBROUTINE FNDIAM(SND1, SND2, NDSTK, NR, NDEG, LVL, LVLS1,
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* LVLS2, IWK, IDFLT)
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C FNDIAM IS THE CONTROL PROCEDURE FOR FINDING THE PSEUDO-DIAMETER OF
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C NDSTK AS WELL AS THE LEVEL STRUCTURE FROM EACH END
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C SND1- ON INPUT THIS IS THE NODE NUMBER OF THE FIRST
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C ATTEMPT AT FINDING A DIAMETER. ON OUTPUT IT
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C CONTAINS THE ACTUAL NUMBER USED.
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C SND2- ON OUTPUT CONTAINS OTHER END OF DIAMETER
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C LVLS1- ARRAY CONTAINING LEVEL STRUCTURE WITH SND1 AS ROOT
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C LVLS2- ARRAY CONTAINING LEVEL STRUCTURE WITH SND2 AS ROOT
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C IDFLT- FLAG USED IN PICKING FINAL LEVEL STRUCTURE, SET
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C =1 IF WIDTH OF LVLS1 .LE. WIDTH OF LVLS2, OTHERWISE =2
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C LVL,IWK- WORKING STORAGE
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C USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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INTEGER NDSTK
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INTEGER FLAG, SND, SND1, SND2
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COMMON /GRA/ N, IDPTH, IDEG
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C IT IS ASSUMED THAT THE LAST LEVEL HAS AT MOST 100 NODES.
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COMMON /CC/ NDLST(10001)
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DIMENSION NDSTK(NR,1), NDEG(1), LVL(1), LVLS1(1), LVLS2(1),
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* IWK(1)
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FLAG = 0
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MTW2 = N
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SND = SND1
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C ZERO LVL TO INDICATE ALL NODES ARE AVAILABLE TO TREE
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10 DO 20 I=1,N
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LVL(I) = 0
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20 CONTINUE
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LVLN = 1
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C DROP A TREE FROM SND
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CALL TREE(SND, NDSTK, NR, LVL, IWK, NDEG, LVLWTH, LVLBOT,
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* LVLN, MAXLW, MTW2)
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IF (FLAG.GE.1) GO TO 50
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FLAG = 1
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30 IDPTH = LVLN - 1
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MTW1 = MAXLW
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C COPY LEVEL STRUCTURE INTO LVLS1
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DO 40 I=1,N
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LVLS1(I) = LVL(I)
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40 CONTINUE
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NDXN = 1
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NDXL = 0
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MTW2 = N
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C SORT LAST LEVEL BY DEGREE AND STORE IN NDLST
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CALL SORTDG(NDLST, IWK(LVLBOT), NDXL, LVLWTH, NDEG)
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SND = NDLST(1)
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GO TO 10
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50 IF (IDPTH.GE.LVLN-1) GO TO 60
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C START AGAIN WITH NEW STARTING NODE
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SND1 = SND
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GO TO 30
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60 IF (MAXLW.GE.MTW2) GO TO 80
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MTW2 = MAXLW
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SND2 = SND
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C STORE NARROWEST REVERSE LEVEL STRUCTURE IN LVLS2
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DO 70 I=1,N
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LVLS2(I) = LVL(I)
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70 CONTINUE
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80 IF (NDXN.EQ.NDXL) GO TO 90
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C TRY NEXT NODE IN NDLST
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NDXN = NDXN + 1
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SND = NDLST(NDXN)
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GO TO 10
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90 IDFLT = 1
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IF (MTW2.LE.MTW1) IDFLT = 2
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RETURN
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END
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SUBROUTINE TREE(IROOT, NDSTK, NR, LVL, IWK, NDEG, LVLWTH,
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* LVLBOT, LVLN, MAXLW, IBORT)
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C TREE DROPS A TREE IN NDSTK FROM IROOT
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C LVL- ARRAY INDICATING AVAILABLE NODES IN NDSTK WITH ZERO
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C ENTRIES. TREE ENTERS LEVEL NUMBERS ASSIGNED
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C DURING EXECUTION OF THIS PROCEDURE
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C IWK- ON OUTPUT CONTAINS NODE NUMBERS USED IN TREE
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C ARRANGED BY LEVELS (IWK(LVLN) CONTAINS IROOT
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C AND IWK(LVLBOT+LVLWTH-1) CONTAINS LAST NODE ENTERED)
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C LVLWTH- ON OUTPUT CONTAINS WIDTH OF LAST LEVEL
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C LVLBOT- ON OUTPUT CONTAINS INDEX INTO IWK OF FIRST
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C NODE IN LAST LEVEL
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C MAXLW- ON OUTPUT CONTAINS THE MAXIMUM LEVEL WIDTH
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C LVLN- ON INPUT THE FIRST AVAILABLE LOCATION IN IWK
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C USUALLY ONE BUT IF IWK IS USED TO STORE PREVIOUS
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C CONNECTED COMPONENTS, LVLN IS NEXT AVAILABLE LOCATION.
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C ON OUTPUT THE TOTAL NUMBER OF LEVELS + 1
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C IBORT- INPUT PARAM WHICH TRIGGERS EARLY RETURN IF
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C MAXLW BECOMES .GE. IBORT
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C USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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INTEGER NDSTK
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DIMENSION NDSTK(NR,1), LVL(1), IWK(1), NDEG(1)
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MAXLW = 0
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ITOP = LVLN
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INOW = LVLN
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LVLBOT = LVLN
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LVLTOP = LVLN + 1
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LVLN = 1
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LVL(IROOT) = 1
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IWK(ITOP) = IROOT
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10 LVLN = LVLN + 1
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20 IWKNOW = IWK(INOW)
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NDROW = NDEG(IWKNOW)
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DO 30 J=1,NDROW
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ITEST = NDSTK(IWKNOW,J)
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IF (LVL(ITEST).NE.0) GO TO 30
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LVL(ITEST) = LVLN
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ITOP = ITOP + 1
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IWK(ITOP) = ITEST
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30 CONTINUE
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INOW = INOW + 1
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IF (INOW.LT.LVLTOP) GO TO 20
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LVLWTH = LVLTOP - LVLBOT
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IF (MAXLW.LT.LVLWTH) MAXLW = LVLWTH
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IF (MAXLW.GE.IBORT) RETURN
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IF (ITOP.LT.LVLTOP) RETURN
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LVLBOT = INOW
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LVLTOP = ITOP + 1
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GO TO 10
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END
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SUBROUTINE SORTDG(STK1, STK2, X1, X2, NDEG)
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C SORTDG SORTS STK2 BY DEGREE OF THE NODE AND ADDS IT TO THE END
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C OF STK1 IN ORDER OF LOWEST TO HIGHEST DEGREE. X1 AND X2 ARE THE
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C NUMBER OF NODES IN STK1 AND STK2 RESPECTIVELY.
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INTEGER X1, X2, STK1, STK2, TEMP
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COMMON /GRA/ N, IDPTH, IDEG
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DIMENSION NDEG(1), STK1(1), STK2(1)
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IND = X2
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10 ITEST = 0
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IND = IND - 1
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IF (IND.LT.1) GO TO 30
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DO 20 I=1,IND
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J = I + 1
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ISTK2 = STK2(I)
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JSTK2 = STK2(J)
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IF (NDEG(ISTK2).LE.NDEG(JSTK2)) GO TO 20
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ITEST = 1
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TEMP = STK2(I)
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STK2(I) = STK2(J)
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STK2(J) = TEMP
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20 CONTINUE
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IF (ITEST.EQ.1) GO TO 10
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30 DO 40 I=1,X2
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X1 = X1 + 1
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STK1(X1) = STK2(I)
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40 CONTINUE
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RETURN
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END
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SUBROUTINE GPS_SETUP(LVL, LVLS1, LVLS2)
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C SETUP COMPUTES THE REVERSE LEVELING INFO FROM LVLS2 AND STORES
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C IT INTO LVLS2. NACUM(I) IS INITIALIZED TO NODES/ITH LEVEL FOR NODES
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C ON THE PSEUDO-DIAMETER OF THE GRAPH. LVL IS INITIALIZED TO NON-
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C ZERO FOR NODES ON THE PSEUDO-DIAM AND NODES IN A DIFFERENT
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C COMPONENT OF THE GRAPH.
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COMMON /GRA/ N, IDPTH, IDEG
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C IT IS ASSUMED THAT THERE ARE AT MOST 100 LEVELS.
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COMMON /LVLW/ NHIGH(10000), NLOW(10000), NACUM(10000)
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DIMENSION LVL(1), LVLS1(1), LVLS2(1)
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DO 10 I=1,IDPTH
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NACUM(I) = 0
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10 CONTINUE
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DO 30 I=1,N
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LVL(I) = 1
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LVLS2(I) = IDPTH + 1 - LVLS2(I)
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ITEMP = LVLS2(I)
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IF (ITEMP.GT.IDPTH) GO TO 30
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IF (ITEMP.NE.LVLS1(I)) GO TO 20
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NACUM(ITEMP) = NACUM(ITEMP) + 1
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GO TO 30
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20 LVL(I) = 0
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30 CONTINUE
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RETURN
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END
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INTEGER FUNCTION SORT2(DMY)
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C SORT2 SORTS SIZE AND STPT INTO DESCENDING ORDER ACCORDING TO
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C VALUES OF SIZE. XC=NUMBER OF ENTRIES IN EACH ARRAY
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INTEGER TEMP, CCSTOR, SIZE, STPT, XC
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C IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
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COMMON /CC/ XC, SIZE(5000), STPT(5000)
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SORT2 = 0
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IF (XC.EQ.0) RETURN
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SORT2 = 1
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IND = XC
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10 ITEST = 0
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IND = IND - 1
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IF (IND.LT.1) RETURN
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DO 20 I=1,IND
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J = I + 1
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IF (SIZE(I).GE.SIZE(J)) GO TO 20
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ITEST = 1
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TEMP = SIZE(I)
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SIZE(I) = SIZE(J)
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SIZE(J) = TEMP
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TEMP = STPT(I)
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STPT(I) = STPT(J)
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STPT(J) = TEMP
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20 CONTINUE
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IF (ITEST.EQ.1) GO TO 10
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RETURN
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END
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SUBROUTINE PIKLVL(LVLS1, LVLS2, CCSTOR, IDFLT, ISDIR)
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C PIKLVL CHOOSES THE LEVEL STRUCTURE USED IN NUMBERING GRAPH
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C LVLS1- ON INPUT CONTAINS FORWARD LEVELING INFO
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C LVLS2- ON INPUT CONTAINS REVERSE LEVELING INFO
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C ON OUTPUT THE FINAL LEVEL STRUCTURE CHOSEN
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C CCSTOR- ON INPUT CONTAINS CONNECTED COMPONENT INFO
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C IDFLT- ON INPUT =1 IF WDTH LVLS1.LE.WDTH LVLS2, =2 OTHERWISE
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C NHIGH KEEPS TRACK OF LEVEL WIDTHS FOR HIGH NUMBERING
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C NLOW- KEEPS TRACK OF LEVEL WIDTHS FOR LOW NUMBERING
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C NACUM- KEEPS TRACK OF LEVEL WIDTHS FOR CHOSEN LEVEL STRUCTURE
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C XC- NUMBER OF CONNECTED COMPONENTS
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C SIZE(I)- SIZE OF ITH CONNECTED COMPONENT
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C STPT(I)- INDEX INTO CCSTORE OF 1ST NODE IN ITH CON COMPT
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C ISDIR- FLAG WHICH INDICATES WHICH WAY THE LARGEST CONNECTED
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C COMPONENT FELL. =+1 IF LOW AND -1 IF HIGH
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INTEGER CCSTOR, SIZE, STPT, XC, END
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COMMON /GRA/ N, IDPTH, IDEG
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C IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 COMPONENTS AND
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C THAT THERE ARE AT MOST 100 LEVELS.
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COMMON /LVLW/ NHIGH(10000), NLOW(10000), NACUM(10000)
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COMMON /CC/ XC, SIZE(5000), STPT(5000)
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DIMENSION LVLS1(1), LVLS2(1), CCSTOR(1)
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C FOR EACH CONNECTED COMPONENT DO
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DO 80 I=1,XC
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J = STPT(I)
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END = SIZE(I) + J - 1
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C SET NHIGH AND NLOW EQUAL TO NACUM
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DO 10 K=1,IDPTH
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NHIGH(K) = NACUM(K)
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NLOW(K) = NACUM(K)
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10 CONTINUE
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C UPDATE NHIGH AND NLOW FOR EACH NODE IN CONNECTED COMPONENT
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DO 20 K=J,END
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INODE = CCSTOR(K)
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LVLNH = LVLS1(INODE)
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NHIGH(LVLNH) = NHIGH(LVLNH) + 1
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LVLNL = LVLS2(INODE)
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NLOW(LVLNL) = NLOW(LVLNL) + 1
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20 CONTINUE
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MAX1 = 0
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MAX2 = 0
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C SET MAX1=LARGEST NEW NUMBER IN NHIGH
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C SET MAX2=LARGEST NEW NUMBER IN NLOW
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DO 30 K=1,IDPTH
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IF (2*NACUM(K).EQ.NLOW(K)+NHIGH(K)) GO TO 30
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IF (NHIGH(K).GT.MAX1) MAX1 = NHIGH(K)
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IF (NLOW(K).GT.MAX2) MAX2 = NLOW(K)
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30 CONTINUE
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C SET IT= NUMBER OF LEVEL STRUCTURE TO BE USED
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IT = 1
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IF (MAX1.GT.MAX2) IT = 2
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IF (MAX1.EQ.MAX2) IT = IDFLT
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IF (IT.EQ.2) GO TO 60
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IF (I.EQ.1) ISDIR = -1
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C COPY LVLS1 INTO LVLS2 FOR EACH NODE IN CONNECTED COMPONENT
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|
DO 40 K=J,END
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INODE = CCSTOR(K)
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|
LVLS2(INODE) = LVLS1(INODE)
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40 CONTINUE
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C UPDATE NACUM TO BE THE SAME AS NHIGH
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|
DO 50 K=1,IDPTH
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NACUM(K) = NHIGH(K)
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50 CONTINUE
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|
GO TO 80
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C UPDATE NACUM TO BE THE SAME AS NLOW
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60 DO 70 K=1,IDPTH
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NACUM(K) = NLOW(K)
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70 CONTINUE
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80 CONTINUE
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RETURN
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END
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SUBROUTINE NUMBER(SND, NUM, NDSTK, LVLS2, NDEG, RENUM, LVLST,
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* LSTPT, NR, NFLG, IBW2, IPF2, IPFA, ISDIR)
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C NUMBER PRODUCES THE NUMBERING OF THE GRAPH FOR MIN BANDWIDTH
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|
C SND- ON INPUT THE NODE TO BEGIN NUMBERING ON
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C NUM- ON INPUT AND OUTPUT, THE NEXT AVAILABLE NUMBER
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|
C LVLS2- THE LEVEL STRUCTURE TO BE USED IN NUMBERING
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|
C RENUM- THE ARRAY USED TO STORE THE NEW NUMBERING
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|
C LVLST- ON OUTPUT CONTAINS LEVEL STRUCTURE
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|
C LSTPT(I)- ON OUTPUT, INDEX INTO LVLST TO FIRST NODE IN ITH LVL
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|
C LSTPT(I+1) - LSTPT(I) = NUMBER OF NODES IN ITH LVL
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|
C NFLG- =+1 IF SND IS FORWARD END OF PSEUDO-DIAM
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|
C =-1 IF SND IS REVERSE END OF PSEUDO-DIAM
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|
C IBW2- BANDWIDTH OF NEW NUMBERING COMPUTED BY NUMBER
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|
C IPF2- PROFILE OF NEW NUMBERING COMPUTED BY NUMBER
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|
C IPFA- WORKING STORAGE USED TO COMPUTE PROFILE AND BANDWIDTH
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|
C ISDIR- INDICATES STEP DIRECTION USED IN NUMBERING(+1 OR -1)
|
|
C USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
|
|
INTEGER NDSTK
|
|
INTEGER SND, STKA, STKB, STKC, STKD, XA, XB, XC, XD, CX, END,
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|
* RENUM, TEST
|
|
COMMON /GRA/ N, IDPTH, IDEG
|
|
C THE STORAGE IN COMMON BLOCKS CC AND LVLW IS NOW FREE AND CAN
|
|
C BE USED FOR STACKS.
|
|
COMMON /LVLW/ STKA(10000), STKB(10000), STKC(10000)
|
|
COMMON /CC/ STKD(10001)
|
|
DIMENSION IPFA(1)
|
|
DIMENSION NDSTK(NR,1), LVLS2(1), NDEG(1), RENUM(1), LVLST(1),
|
|
* LSTPT(1)
|
|
C SET UP LVLST AND LSTPT FROM LVLS2
|
|
DO 10 I=1,N
|
|
IPFA(I) = 0
|
|
10 CONTINUE
|
|
write(0,*) 'NUMBER: initialization on NSTPT'
|
|
NSTPT = 1
|
|
DO 30 I=1,IDPTH
|
|
LSTPT(I) = NSTPT
|
|
DO 20 J=1,N
|
|
IF (LVLS2(J).NE.I) GO TO 20
|
|
LVLST(NSTPT) = J
|
|
NSTPT = NSTPT + 1
|
|
20 CONTINUE
|
|
30 CONTINUE
|
|
LSTPT(IDPTH+1) = NSTPT
|
|
write(0,*) 'NUMBER: initialization completed', idpth,nstpt
|
|
C STKA, STKB, STKC AND STKD ARE STACKS WITH POINTERS
|
|
C XA,XB,XC, AND XD. CX IS A SPECIAL POINTER INTO STKC WHICH
|
|
C INDICATES THE PARTICULAR NODE BEING PROCESSED.
|
|
C LVLN KEEPS TRACK OF THE LEVEL WE ARE WORKING AT.
|
|
C INITIALLY STKC CONTAINS ONLY THE INITIAL NODE, SND.
|
|
LVLN = 0
|
|
IF (NFLG.LT.0) LVLN = IDPTH + 1
|
|
XC = 1
|
|
STKC(XC) = SND
|
|
40 CX = 1
|
|
XD = 0
|
|
LVLN = LVLN + NFLG
|
|
LST = LSTPT(LVLN)
|
|
LND = LSTPT(LVLN+1) - 1
|
|
C BEGIN PROCESSING NODE STKC(CX)
|
|
50 IPRO = STKC(CX)
|
|
RENUM(IPRO) = NUM
|
|
NUM = NUM + ISDIR
|
|
END = NDEG(IPRO)
|
|
XA = 0
|
|
XB = 0
|
|
C CHECK ALL ADJACENT NODES
|
|
DO 80 I=1,END
|
|
c$$$ write(0,*) 'NUMBER: loop 80 ',i,end, lvln
|
|
TEST = NDSTK(IPRO,I)
|
|
INX = RENUM(TEST)
|
|
C ONLY NODES NOT NUMBERED OR ALREADY ON A STACK ARE ADDED
|
|
IF (INX.EQ.0) GO TO 60
|
|
IF (INX.LT.0) GO TO 80
|
|
C DO PRELIMINARY BANDWIDTH AND PROFILE CALCULATIONS
|
|
NBW = (RENUM(IPRO)-INX)*ISDIR
|
|
IF (ISDIR.GT.0) INX = RENUM(IPRO)
|
|
IF (IPFA(INX).LT.NBW) IPFA(INX) = NBW
|
|
GO TO 80
|
|
60 RENUM(TEST) = -1
|
|
C PUT NODES ON SAME LEVEL ON STKA, ALL OTHERS ON STKB
|
|
IF (LVLS2(TEST).EQ.LVLS2(IPRO)) GO TO 70
|
|
XB = XB + 1
|
|
if (xb>10000) write(0,*) 'XB>10000 in NUMBER'
|
|
STKB(XB) = TEST
|
|
GO TO 80
|
|
70 XA = XA + 1
|
|
if (xa>10000) write(0,*) 'XA>10000 in NUMBER'
|
|
STKA(XA) = TEST
|
|
80 CONTINUE
|
|
C SORT STKA AND STKB INTO INCREASING DEGREE AND ADD STKA TO STKC
|
|
C AND STKB TO STKD
|
|
IF (XA.EQ.0) GO TO 100
|
|
IF (XA.EQ.1) GO TO 90
|
|
CALL SORTDG(STKC, STKA, XC, XA, NDEG)
|
|
GO TO 100
|
|
90 XC = XC + 1
|
|
if (xc>10000) write(0,*) 'XC>10000 in NUMBER'
|
|
STKC(XC) = STKA(XA)
|
|
|
|
100 IF (XB.EQ.0) GO TO 120
|
|
IF (XB.EQ.1) GO TO 110
|
|
CALL SORTDG(STKD, STKB, XD, XB, NDEG)
|
|
GO TO 120
|
|
110 XD = XD + 1
|
|
if (xd>10000) write(0,*) 'XD>10000 in NUMBER'
|
|
STKD(XD) = STKB(XB)
|
|
C BE SURE TO PROCESS ALL NODES IN STKC
|
|
120 CX = CX + 1
|
|
if (cx>10000) write(0,*) 'CX>10000 in NUMBER'
|
|
IF (XC.GE.CX) GO TO 50
|
|
C WHEN STKC IS EXHAUSTED LOOK FOR MIN DEGREE NODE IN SAME LEVEL
|
|
C WHICH HAS NOT BEEN PROCESSED
|
|
MAX = IDEG + 1
|
|
SND = N + 1
|
|
DO 130 I=LST,LND
|
|
TEST = LVLST(I)
|
|
IF (RENUM(TEST).NE.0) GO TO 130
|
|
IF (NDEG(TEST).GE.MAX) GO TO 130
|
|
RENUM(SND) = 0
|
|
RENUM(TEST) = -1
|
|
MAX = NDEG(TEST)
|
|
SND = TEST
|
|
130 CONTINUE
|
|
IF (SND.EQ.N+1) GO TO 140
|
|
XC = XC + 1
|
|
if (xc>10000) write(0,*) 'XC>10000 ...2... in NUMBER'
|
|
STKC(XC) = SND
|
|
GO TO 50
|
|
C IF STKD IS EMPTY WE ARE DONE, OTHERWISE COPY STKD ONTO STKC
|
|
C AND BEGIN PROCESSING NEW STKC
|
|
140 IF (XD.EQ.0) GO TO 160
|
|
DO 150 I=1,XD
|
|
STKC(I) = STKD(I)
|
|
150 CONTINUE
|
|
XC = XD
|
|
GO TO 40
|
|
C DO FINAL BANDWIDTH AND PROFILE CALCULATIONS
|
|
160 DO 170 I=1,N
|
|
IF (IPFA(I).GT.IBW2) IBW2 = IPFA(I)
|
|
IPF2 = IPF2 + IPFA(I)
|
|
170 CONTINUE
|
|
RETURN
|
|
END
|