| 1 |
gross |
505 |
/* Finley_Reduce determines a row and column permutation which, when applied to a given sparse matrix, produces a permuted */ |
| 2 |
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/* matrix with a smaller bandwidth and profile. the input array is a connection table which represents the */ |
| 3 |
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/* indices of the nonzero elements of the matrix, a. the algorithm is described in terms of the adjacency graph which */ |
| 4 |
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/* has the characteristic that there is an edge (connection) between nodes i and j if a(i,j) .ne. 0 and i .ne. j. */ |
| 5 |
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| 6 |
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| 7 |
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/* NDSTK(NR,D1) D1 IS >= MAXIMUM DEGREE OF ALL NODES. |
| 8 |
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/* Label(D2) D2 AND NR ARE >= THE TOTAL NUMBER OF |
| 9 |
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/* NewLabel(D2+1) NODES IN THE GRAPH. |
| 10 |
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/* Degree(D2) STORAGE REQUIREMENTS CAN BE SIGNifICANTLY |
| 11 |
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| 12 |
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/* AssignedLevel(D2) DECREASED FOR IBM 360 AND 370 COMPUTERS |
| 13 |
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/* LevelToNode(D2) BY REPLACING INTEGER NDSTK BY |
| 14 |
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/* NodeToLevel(D2) INTEGER*2 NDSTK IN SUBROUTINES Finley_Reduce, |
| 15 |
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/* ConnectedComponents(D2) Finley_Reduce_setDegree, Finley_Reduce_findDiameter, Finley_Reduce_dropTree AND NUMBER. |
| 16 |
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/* COMMON INFORMATION--THE FOLLOWING COMMON BLOCK MUST BE IN THE |
| 17 |
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/* CALLING ROUTINE. |
| 18 |
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/* COMMON/GRA/N,IDPTH,ndeg_max |
| 19 |
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/* EXPLANATION OF INPUT VARIABLES-- |
| 20 |
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/* NDSTK- CONNECTION TABLE REPRESENTING GRAPH. |
| 21 |
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/* pattern->index[iptr]=NODE NUMBER OF JTH CONNECTION TO NODE |
| 22 |
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/* NUMBER I. A CONNECTION OF A NODE TO ITSELF IS NOT |
| 23 |
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/* LISTED. EXTRA POSITIONS MUST HAVE ZERO FILL. |
| 24 |
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/* NR- ROW DIMENSION ASSIGNED NDSTK IN CALLING PROGRAM. |
| 25 |
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/* Label[i]- NUMBERING OF ITH NODE UPON INPUT. if NO NUMBERING EXISTS THEN Label[i]=I. |
| 26 |
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/* N- NUMBER OF NODES IN GRAPH (EQUAL TO ORDER OF MATRIX). |
| 27 |
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/* ndeg_max- MAXIMUM DEGREE OF ANY NODE IN THE GRAPH. |
| 28 |
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/* Degree[i]- THE DEGREE OF THE ITH NODE. |
| 29 |
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/* EXPLANATION OF OUTPUT VARIABLES-- |
| 30 |
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/* NewLabel[i]- THE NEW NUMBER FOR THE ITH NODE. |
| 31 |
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/* newBandwidth- THE BANDWIDTH AFTER numbering . |
| 32 |
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/* newProfile- THE PROFILE AFTER numbering . |
| 33 |
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/* IDPTH- NUMBER OF LEVELS IN Finley_Reduce LEVEL STRUCTURE. |
| 34 |
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/* */ |
| 35 |
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/* The following only have meaning if the graph was connected: |
| 36 |
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| 37 |
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/* AssignedLevel[i]- INDEX INTO LevelToNode TO THE FIRST NODE IN LEVEL I. AssignedLevel(I+1)-AssignedLevel[i]= number of nodes in ith leveL |
| 38 |
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/* LevelToNode- node numbers listed by level |
| 39 |
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/* NodeToLevel[i]- the level assigned to node i by Finley_Reduce. |
| 40 |
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| 41 |
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/* WORKING STORAGE VARIABLE-- |
| 42 |
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/* ConnectedComponents |
| 43 |
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/* LOCAL STORAGE-- |
| 44 |
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/* COMMON/CC/-SUBROUTINES Finley_Reduce, SORT2 AND PIKAssignedLevel ASSUME THAT |
| 45 |
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/* THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
| 46 |
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/* SUBROUTINE Finley_Reduce_findDiameter ASSUMES THAT THERE ARE AT MOST |
| 47 |
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/* 100 NODES IN THE LAST LEVEL. |
| 48 |
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/* COMMON/AssignedLevelW/-SUBROUTINES Finley_Reduce_setup AND PIKAssignedLevel ASSUME THAT THERE |
| 49 |
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/* ARE AT MOST 100 LEVELS. |
| 50 |
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SUBROUTINE Finley_Reduce(NDSTK, NR, Label, NewLabel, Degree, AssignedLevel, LevelToNode,NodeToLevel, ConnectedComponents, newBandwidth, newProfile, NIN, ndeg_maxIN) |
| 51 |
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/* USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. |
| 52 |
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integer NIN, ndeg_maxIN |
| 53 |
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INTEGER NDSTK |
| 54 |
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INTEGER StartNode, ReverseNode, NewLabel, ConnectedComponentCounter, SORT2, LastAvailableNodeNumber, ConnectedComponents, |
| 55 |
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* SIZE, STPT, FirstAvailableNodeNumber |
| 56 |
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COMMON /GRA/ N, IDPTH, ndeg_max |
| 57 |
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/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
| 58 |
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COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
| 59 |
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COMMON /AssignedLevelW/ NHIGH(100), NLOW(100), NACUM(100) |
| 60 |
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DIMENSION ConnectedComponents(1), Label(1) |
| 61 |
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DIMENSION NDSTK(NR,1), AssignedLevel(1), LevelToNode(1), NodeToLevel(1), NewLabel(1), |
| 62 |
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* Degree(1) |
| 63 |
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newBandwidth = 0 |
| 64 |
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newProfile = 0 |
| 65 |
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/* SET NewLabel[i]=0 FOR ALL I TO INDICATE NODE I IS UNNUMBERED |
| 66 |
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c |
| 67 |
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c N = NR |
| 68 |
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c do i=0,i<N,++i) |
| 69 |
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c if(ndeg_max<Degree[i]) then |
| 70 |
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c ndeg_max = Degree[i] |
| 71 |
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c end if |
| 72 |
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c end do |
| 73 |
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c |
| 74 |
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| 75 |
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set Degree |
| 76 |
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N=NIN |
| 77 |
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ndeg_max = ndeg_maxIN |
| 78 |
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for (i=0,i<N,++i) { |
| 79 |
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Degree[i]=ptr[i+1]-ptr[i]; |
| 80 |
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NewLabel[i] = 0; |
| 81 |
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} |
| 82 |
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| 83 |
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/* COMPUTE DEGREE OF EACH NODE AND ORIGINAL BANDWIDTH AND PROFILE*/ |
| 84 |
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| 85 |
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CALL Finley_Reduce_setDegree(NDSTK, NR, Degree, Label, initialBandwidth, initialProfile) |
| 86 |
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| 87 |
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/* FirstAvailableNodeNumber = low end of available numbers for numbering */ |
| 88 |
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/* LastAvailableNodeNumber = high end of available numbers for numbering */ |
| 89 |
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FirstAvailableNodeNumber = 1; |
| 90 |
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LastAvailableNodeNumber = N; |
| 91 |
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| 92 |
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/* number the nodes of degree zero */ |
| 93 |
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| 94 |
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for (i=0,i<N,++i) { |
| 95 |
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if (Degree[i]==0) { |
| 96 |
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NewLabel[i] = LastAvailableNodeNumber; |
| 97 |
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LastAvailableNodeNumber--; |
| 98 |
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} |
| 99 |
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} |
| 100 |
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/* find an unnumbered node of min degree to start on */ |
| 101 |
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while (FirstAvailableNodeNumber<=LastAvailableNodeNumber) { |
| 102 |
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| 103 |
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LowestDegree = ndeg_max + 1; |
| 104 |
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Flag = 1; |
| 105 |
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SDIR = 1; |
| 106 |
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for (i=0,i<N,++i) { |
| 107 |
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if (Degree[i]<LowestDegree && NewLabel[i]<=0) { |
| 108 |
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LowestDegree = Degree[i]; |
| 109 |
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StartNode = i; |
| 110 |
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} |
| 111 |
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} |
| 112 |
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| 113 |
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/* find pseudo-diameter and associated level structures: */ |
| 114 |
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| 115 |
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/* StartNode and ReverseNode are the ends of the diameter and LevelToNode and NodeToLevel are the respective level structures. */ |
| 116 |
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| 117 |
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CALL Finley_Reduce_findDiameter(StartNode, ReverseNode, NDSTK, NR, Degree, AssignedLevel, LevelToNode,NodeToLevel, ConnectedComponents, IDFLT) |
| 118 |
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/* Flag INDICATES THE END TO BEGIN NUMBERING ON */ |
| 119 |
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if (Degree(StartNode)>Degree(ReverseNode)) { |
| 120 |
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Flag = -1; |
| 121 |
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StartNode = ReverseNode; |
| 122 |
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} |
| 123 |
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CALL Finley_Reduce_setup(AssignedLevel, LevelToNode, NodeToLevel) |
| 124 |
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/* find all the connected components (ConnectedComponentCounter counts them) */ |
| 125 |
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ConnectedComponentCounter = 0; |
| 126 |
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LROOT = 1 |
| 127 |
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available_NodesInTree = 1 |
| 128 |
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for (i=0,i<N,++i) { |
| 129 |
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if (AssignedLevel[i]==0) { |
| 130 |
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ConnectedComponentCounter++; |
| 131 |
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STPT(ConnectedComponentCounter) = LROOT |
| 132 |
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CALL Finley_Reduce_dropTree(I, NDSTK, NR, AssignedLevel, ConnectedComponents, Degree, LastLevelWidth, BottomLevel,available_NodesInTree, max_LevelWidth, N) |
| 133 |
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SIZE(ConnectedComponentCounter) = BottomLevel + LastLevelWidth - LROOT |
| 134 |
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LROOT = BottomLevel + LastLevelWidth |
| 135 |
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available_NodesInTree = LROOT |
| 136 |
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} |
| 137 |
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} |
| 138 |
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/* on return from PIKAssignedLevel, DirectionLargestComponent indicates the direction the largest component fell. */ |
| 139 |
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/* DirectionLargestComponent is modIFied now to indicate the numbering direction. num is set to the proper value for this direction. */ |
| 140 |
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if (SORT2(DMY)!=0) PIKAssignedLevel(LevelToNode, NodeToLevel, ConnectedComponents, IDFLT, DirectionLargestComponent) |
| 141 |
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DirectionLargestComponent = DirectionLargestComponent*Flag; |
| 142 |
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NUM= (DirectionLargestComponent<0) ? LastAvailableNodeNumber :FirstAvailableNodeNumber; |
| 143 |
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| 144 |
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CALL NUMBER(StartNode, NUM, NDSTK, NodeToLevel, Degree, NewLabel, LevelToNode, |
| 145 |
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* AssignedLevel, NR, Flag, newBandwidth, newProfile, ConnectedComponents, DirectionLargestComponent) |
| 146 |
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| 147 |
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/* update LastAvailableNodeNumber or FirstAvailableNodeNumber after numbering */ |
| 148 |
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| 149 |
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if (DirectionLargestComponent<0) LastAvailableNodeNumber = NUM; |
| 150 |
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if (DirectionLargestComponent>0) FirstAvailableNodeNumber = NUM; |
| 151 |
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| 152 |
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} |
| 153 |
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| 154 |
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/* if original numbering is better than new one, set up to return it */ |
| 155 |
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| 156 |
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if (newBandwidth > initialBandwidth) { |
| 157 |
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for (i=0,i<N,++i) |
| 158 |
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NewLabel[i] = Label[i]; |
| 159 |
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*newBandwidth = initialBandwidth; |
| 160 |
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*newProfile = initialProfile; |
| 161 |
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} |
| 162 |
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} |
| 163 |
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| 164 |
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/* Finley_Reduce_setDegree computes the degree of each node and stores it in the array Degree. */ |
| 165 |
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/* the bandwidth and profile for the original or input numbering of the graph is computed also. */ |
| 166 |
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| 167 |
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void Finley_Reduce_setDegree( pattern, dim_t *Degree,dim_t* Label,dim_t *bandwidth,dim_t *initialProfile) { |
| 168 |
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| 169 |
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*bandwidth = 0; |
| 170 |
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*profile = 0; |
| 171 |
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for (i=0,i<pattern->N,++i) { |
| 172 |
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Degree[i] = 0; |
| 173 |
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max_diff = 0; |
| 174 |
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for (iptr=pattern->ptr[i],iptr<pattern->ptr[i+1],++i) { |
| 175 |
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Degree[i] = Degree[i] + 1; |
| 176 |
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diff = Label[i] - Label(pattern->index[iptr]); |
| 177 |
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max_diff = MAX(max_diff,diff); |
| 178 |
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} |
| 179 |
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*profile + = max_diff; |
| 180 |
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*bandwidth=MAX(*bandwidth,max_diff); |
| 181 |
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} |
| 182 |
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} |
| 183 |
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/* Finley_Reduce_findDiameter is the control procedure for finding the pseudo-diameter of pattern */ |
| 184 |
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/* as well as the level structure from each end */ |
| 185 |
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| 186 |
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/* StartNode- on input this is the node number of the first attempt at finding a diaMeter. */ |
| 187 |
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/* on output it contains the actual number used. |
| 188 |
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/* EndNode- on output contains other end of diameter |
| 189 |
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/* LevelToNode- ARRAY CONTAINING LEVEL STRUCTURE WITH StartNode AS ROOT |
| 190 |
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/* NodeToLevel- ARRAY CONTAINING LEVEL STRUCTURE WITH EndNode AS ROOT |
| 191 |
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/* IDFLT- FLAG USED IN PICKING FINAL LEVEL STRUCTURE, SET |
| 192 |
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/* =1 if WIDTH OF LevelToNode <= WIDTH OF NodeToLevel, OTHERWISE =2 |
| 193 |
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/* AssignedLevel,NodesInTree- WORKING STORAGE |
| 194 |
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void Finley_Reduce_findDiameter(index_t *StartNode,index_t *EndNode,PPP pattern, NR, Degree, AssignedLevel, LevelToNode,NodeToLevel, NodesInTree, IDFLT) |
| 195 |
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INTEGER NDSTK |
| 196 |
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INTEGER FLAG, StartNode2, StartNode, EndNode |
| 197 |
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COMMON /GRA/ N, IDPTH, ndeg_max |
| 198 |
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/* IT IS ASSUMED THAT THE LAST LEVEL HAS AT MOST 100 NODES. |
| 199 |
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COMMON /CC/ NDLST(100) |
| 200 |
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DIMENSION NDSTK(NR,1), Degree(1), AssignedLevel(1), LevelToNode(1), NodeToLevel(1),NodesInTree(1) |
| 201 |
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FLAG = 0; |
| 202 |
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MTW2 = N; |
| 203 |
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StartNode2 = StartNode; |
| 204 |
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10 |
| 205 |
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/* zero AssignedLevel to indicate all nodes are available to Finley_Reduce_dropTree */ |
| 206 |
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for (i=0,i<N,++i) |
| 207 |
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AssignedLevel[i] = 0; |
| 208 |
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| 209 |
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available_NodesInTree = 1 |
| 210 |
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/* drop a tree from StartNode2 */ |
| 211 |
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CALL Finley_Reduce_dropTree(StartNode2, NDSTK, NR, AssignedLevel, NodesInTree, Degree, LastLevelWidth, BottomLevel,available_NodesInTree, max_LevelWidth, MTW2) |
| 212 |
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if (FLAG<1) { |
| 213 |
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FLAG = 1 |
| 214 |
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30 IDPTH = available_NodesInTree - 1 |
| 215 |
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MTW1 = max_LevelWidth |
| 216 |
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/* copy level structure into LevelToNode */ |
| 217 |
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for (i=0,i<N,++i) |
| 218 |
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LevelToNode[i] = AssignedLevel[i]; |
| 219 |
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NDXN = 1; |
| 220 |
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NDXL = 0; |
| 221 |
|
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MTW2 = N; |
| 222 |
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/* sort last level by degree and store in ndlst |
| 223 |
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CALL SORTDG(NDLST, NodesInTree(BottomLevel), NDXL, LastLevelWidth, Degree) |
| 224 |
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StartNode2 = NDLST(1) |
| 225 |
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GO TO 10 |
| 226 |
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} |
| 227 |
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50 if (IDPTH>=available_NodesInTree-1) GO TO 60 |
| 228 |
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/* START AGAIN WITH NEW STARTING NODE |
| 229 |
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StartNode = StartNode2 |
| 230 |
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GO TO 30 |
| 231 |
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60 if (max_LevelWidth>=MTW2) GO TO 80 |
| 232 |
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MTW2 = max_LevelWidth |
| 233 |
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EndNode = StartNode2 |
| 234 |
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/* STORE NARROWEST REVERSE LEVEL STRUCTURE IN NodeToLevel |
| 235 |
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for (70 i=0,i<N,++i) |
| 236 |
|
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NodeToLevel[i] = AssignedLevel[i] |
| 237 |
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70 CONTINUE |
| 238 |
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80 if (NDXN.EQ.NDXL) GO TO 90 |
| 239 |
|
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/* TRY NEXT NODE IN NDLST |
| 240 |
|
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NDXN = NDXN + 1 |
| 241 |
|
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StartNode2 = NDLST(NDXN) |
| 242 |
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GO TO 10 |
| 243 |
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90 IDFLT = 1 |
| 244 |
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if (MTW2<=MTW1) IDFLT = 2 |
| 245 |
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RETURN |
| 246 |
|
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END |
| 247 |
|
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*/ |
| 248 |
|
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void Finley_Reduce_dropTree(index_t root, PPP pattern, NR, index_t *AssignedLevel,index_t *NodesInTree, |
| 249 |
|
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index_t *LastLevelWidth, index_t *BottomLevel,index_t *available_NodesInTree, index_t *max_LevelWidth, index_t max_LevelWidth_abort) |
| 250 |
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| 251 |
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/* Finley_Reduce_dropTree drops a tree in pattern from root */ |
| 252 |
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| 253 |
|
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/* AssignedLevel- array of length length pattern->N indicating available nodes with zero entries. */ |
| 254 |
|
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/* Finley_Reduce_dropTree enters level numbers assigned during execution of this procedure */ |
| 255 |
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| 256 |
|
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/* NodesInTree - on output contains node numbers used in tree (array of length pattern->N) */ |
| 257 |
|
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/* arranged by levels (NodesInTree[available_NodesInTree] contains root and NodesInTree(BottomLevel+LastLevelWidth-1) */ |
| 258 |
|
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/* contains last node entered) */ |
| 259 |
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| 260 |
|
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/* LastLevelWidth - on output contains width of last level */ |
| 261 |
|
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/* BottomLevel - on output contains index into iwk of first node in last level |
| 262 |
|
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/* max_LevelWidth - on output contains the maximum level width |
| 263 |
|
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/* available_NodesInTree- on input the first available location in NodesInTree |
| 264 |
|
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/* usually one but if NodesInTree is used to store previous connected components, */ |
| 265 |
|
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/* available_NodesInTree is next available location. on output the total number of levels + 1 */ |
| 266 |
|
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/* max_LevelWidth_abort- input param which triggers early return if max_LevelWidth becomes >= max_LevelWidth_abort */ |
| 267 |
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|
|
| 268 |
|
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index_t ITOP = available_NodesInTree; |
| 269 |
|
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index_t INOW = available_NodesInTree; |
| 270 |
|
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|
| 271 |
|
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*max_LevelWidth = 0; |
| 272 |
|
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*BottomLevel = available_NodesInTree; |
| 273 |
|
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*TopLevel = available_NodesInTree + 1; |
| 274 |
|
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*available_NodesInTree = 1 |
| 275 |
|
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AssignedLevel(root) = 1 |
| 276 |
|
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NodesInTree(ITOP) = root |
| 277 |
|
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while(max_LevelWidth<max_LevelWidth_abort && ITOP>=TopLevel) { |
| 278 |
|
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available_NodesInTree++; |
| 279 |
|
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while (INOW>=TopLevel) { |
| 280 |
|
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NodesInTreeNOW = NodesInTree(INOW) |
| 281 |
|
|
for (j=pattern->iptr[NodesInTreeNOW],j<pattern->iptr[NodesInTreeNOW+1],++J) { |
| 282 |
|
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ITEST = pattern->index[J]; |
| 283 |
|
|
if (AssignedLevel(ITEST)==0) { |
| 284 |
|
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AssignedLevel(ITEST) = available_NodesInTree; |
| 285 |
|
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ITOP++; |
| 286 |
|
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NodesInTree(ITOP) = ITEST |
| 287 |
|
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} |
| 288 |
|
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} |
| 289 |
|
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INOW = INOW + 1 |
| 290 |
|
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} |
| 291 |
|
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*LastLevelWidth = TopLevel - BottomLevel |
| 292 |
|
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*max_LevelWidth = MAX(max_LevelWidth,LastLevelWidth); |
| 293 |
|
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*BottomLevel = INOW |
| 294 |
|
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*TopLevel = ITOP + 1 |
| 295 |
|
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} |
| 296 |
|
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} |
| 297 |
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| 298 |
|
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SUBROUTINE SORTDG(STK1, STK2, X1, X2, Degree) SOR 10 |
| 299 |
|
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/* SORTDG SORTS STK2 BY DEGREE OF THE NODE AND ADDS IT TO THE END |
| 300 |
|
|
/* OF STK1 IN ORDER OF LOWEST TO HIGHEST DEGREE. X1 AND X2 ARE THE |
| 301 |
|
|
/* NUMBER OF NODES IN STK1 AND STK2 RESPECTIVELY. |
| 302 |
|
|
INTEGER X1, X2, STK1, STK2, TEMP |
| 303 |
|
|
COMMON /GRA/ N, IDPTH, ndeg_max |
| 304 |
|
|
DIMENSION Degree(1), STK1(1), STK2(1) |
| 305 |
|
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IND = X2 |
| 306 |
|
|
10 ITEST = 0 |
| 307 |
|
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IND = IND - 1 |
| 308 |
|
|
if (IND<1) GO TO 30 |
| 309 |
|
|
for (20 I=1,IND |
| 310 |
|
|
J = I + 1 |
| 311 |
|
|
ISTK2 = STK2[i] |
| 312 |
|
|
JSTK2 = STK2(J) |
| 313 |
|
|
if (Degree(ISTK2)<=Degree(JSTK2)) GO TO 20 |
| 314 |
|
|
ITEST = 1 |
| 315 |
|
|
TEMP = STK2[i] |
| 316 |
|
|
STK2[i] = STK2(J) |
| 317 |
|
|
STK2(J) = TEMP |
| 318 |
|
|
20 CONTINUE |
| 319 |
|
|
if (ITEST.EQ.1) GO TO 10 |
| 320 |
|
|
30 for (40 I=1,X2 |
| 321 |
|
|
X1 = X1 + 1 |
| 322 |
|
|
STK1(X1) = STK2[i] |
| 323 |
|
|
40 CONTINUE |
| 324 |
|
|
RETURN |
| 325 |
|
|
END |
| 326 |
|
|
SUBROUTINE Finley_Reduce_setup(AssignedLevel, LevelToNode, NodeToLevel) SET 10 |
| 327 |
|
|
/* Finley_Reduce_setup COMPUTES THE REVERSE LEVELING INFO FROM NodeToLevel AND STORES |
| 328 |
|
|
/* IT INTO NodeToLevel. NACUM[i] IS INITIALIZED TO NODES/ITH LEVEL FOR NODES |
| 329 |
|
|
/* ON THE PSEUDO-diameter OF THE GRAPH. AssignedLevel IS INITIALIZED TO NON- |
| 330 |
|
|
/* ZERO FOR NODES ON THE PSEUDO-diameter AND NODES IN A DifFERENT |
| 331 |
|
|
/* COMPONENT OF THE GRAPH. |
| 332 |
|
|
COMMON /GRA/ N, IDPTH, ndeg_max |
| 333 |
|
|
/* IT IS ASSUMED THAT THERE ARE AT MOST 100 LEVELS. |
| 334 |
|
|
COMMON /AssignedLevelW/ NHIGH(100), NLOW(100), NACUM(100) |
| 335 |
|
|
DIMENSION AssignedLevel(1), LevelToNode(1), NodeToLevel(1) |
| 336 |
|
|
for (10 I=1,IDPTH |
| 337 |
|
|
NACUM[i] = 0 |
| 338 |
|
|
10 CONTINUE |
| 339 |
|
|
for (30 i=0,i<N,++i) |
| 340 |
|
|
AssignedLevel[i] = 1 |
| 341 |
|
|
NodeToLevel[i] = IDPTH + 1 - NodeToLevel[i] |
| 342 |
|
|
ITEMP = NodeToLevel[i] |
| 343 |
|
|
if (ITEMP>IDPTH) GO TO 30 |
| 344 |
|
|
if (ITEMP!=LevelToNode[i]) GO TO 20 |
| 345 |
|
|
NACUM(ITEMP) = NACUM(ITEMP) + 1 |
| 346 |
|
|
GO TO 30 |
| 347 |
|
|
20 AssignedLevel[i] = 0 |
| 348 |
|
|
30 CONTINUE |
| 349 |
|
|
RETURN |
| 350 |
|
|
END |
| 351 |
|
|
INTEGER FUNCTION SORT2(DMY) SOR 10 |
| 352 |
|
|
/* SORT2 SORTS SIZE AND STPT INTO DESCENDING ORDER ACCORDING TO |
| 353 |
|
|
/* VALUES OF SIZE. ConnectedComponentCounter=NUMBER OF ENTRIES IN EACH ARRAY |
| 354 |
|
|
INTEGER TEMP, ConnectedComponents, SIZE, STPT, ConnectedComponentCounter |
| 355 |
|
|
/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
| 356 |
|
|
COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
| 357 |
|
|
SORT2 = 0 |
| 358 |
|
|
if (ConnectedComponentCounter.EQ.0) RETURN |
| 359 |
|
|
SORT2 = 1 |
| 360 |
|
|
IND = ConnectedComponentCounter |
| 361 |
|
|
10 ITEST = 0 |
| 362 |
|
|
IND = IND - 1 |
| 363 |
|
|
if (IND<1) RETURN |
| 364 |
|
|
for (20 I=1,IND |
| 365 |
|
|
J = I + 1 |
| 366 |
|
|
if (SIZE[i]>=SIZE(J)) GO TO 20 |
| 367 |
|
|
ITEST = 1 |
| 368 |
|
|
TEMP = SIZE[i] |
| 369 |
|
|
SIZE[i] = SIZE(J) |
| 370 |
|
|
SIZE(J) = TEMP |
| 371 |
|
|
TEMP = STPT[i] |
| 372 |
|
|
STPT[i] = STPT(J) |
| 373 |
|
|
STPT(J) = TEMP |
| 374 |
|
|
20 CONTINUE |
| 375 |
|
|
if (ITEST.EQ.1) GO TO 10 |
| 376 |
|
|
RETURN |
| 377 |
|
|
END |
| 378 |
|
|
SUBROUTINE PIKAssignedLevel(LevelToNode, NodeToLevel, ConnectedComponents, IDFLT, DirectionLargestComponent) PIK 10 |
| 379 |
|
|
/* PIKAssignedLevel CHOOSES THE LEVEL STRUCTURE USED IN NUMBERING GRAPH |
| 380 |
|
|
/* LevelToNode- ON INPUT CONTAINS FORWARD LEVELING INFO |
| 381 |
|
|
/* NodeToLevel- ON INPUT CONTAINS REVERSE LEVELING INFO |
| 382 |
|
|
/* ON OUTPUT THE FINAL LEVEL STRUCTURE CHOSEN |
| 383 |
|
|
/* ConnectedComponents- ON INPUT CONTAINS CONNECTED COMPONENT INFO |
| 384 |
|
|
/* IDFLT- ON INPUT =1 if WDTH LevelToNode<=WDTH NodeToLevel, =2 OTHERWISE |
| 385 |
|
|
/* NHIGH KEEPS TRACK OF LEVEL WIDTHS FOR HIGH NUMBERING |
| 386 |
|
|
/* NLOW- KEEPS TRACK OF LEVEL WIDTHS FOR LOW NUMBERING |
| 387 |
|
|
/* NACUM- KEEPS TRACK OF LEVEL WIDTHS FOR CHOSEN LEVEL STRUCTURE |
| 388 |
|
|
/* ConnectedComponentCounter- NUMBER OF CONNECTED COMPONENTS |
| 389 |
|
|
/* SIZE[i]- SIZE OF ITH CONNECTED COMPONENT |
| 390 |
|
|
/* STPT[i]- INDEX INTO ConnectedComponentsE OF 1ST NODE IN ITH CON COMPT |
| 391 |
|
|
/* DirectionLargestComponent- FLAG WHICH INDICATES WHICH WAY THE LARGEST CONNECTED |
| 392 |
|
|
/* COMPONENT FELL. =+1 if LOW AND -1 if HIGH |
| 393 |
|
|
INTEGER ConnectedComponents, SIZE, STPT, ConnectedComponentCounter, END |
| 394 |
|
|
COMMON /GRA/ N, IDPTH, ndeg_max |
| 395 |
|
|
/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 COMPONENTS AND |
| 396 |
|
|
/* THAT THERE ARE AT MOST 100 LEVELS. |
| 397 |
|
|
COMMON /AssignedLevelW/ NHIGH(100), NLOW(100), NACUM(100) |
| 398 |
|
|
COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
| 399 |
|
|
DIMENSION LevelToNode(1), NodeToLevel(1), ConnectedComponents(1) |
| 400 |
|
|
/* FOR EACH CONNECTED COMPONENT DO |
| 401 |
|
|
for (80 I=1,ConnectedComponentCounter |
| 402 |
|
|
J = STPT[i] |
| 403 |
|
|
END = SIZE[i] + J - 1 |
| 404 |
|
|
/* SET NHIGH AND NLOW EQUAL TO NACUM |
| 405 |
|
|
for (10 K=1,IDPTH |
| 406 |
|
|
NHIGH(K) = NACUM(K) |
| 407 |
|
|
NLOW(K) = NACUM(K) |
| 408 |
|
|
10 CONTINUE |
| 409 |
|
|
/* UPDATE NHIGH AND NLOW FOR EACH NODE IN CONNECTED COMPONENT |
| 410 |
|
|
for (20 K=J,END |
| 411 |
|
|
INODE = ConnectedComponents(K) |
| 412 |
|
|
available_NodesInTreeH = LevelToNode(INODE) |
| 413 |
|
|
NHIGH(available_NodesInTreeH) = NHIGH(available_NodesInTreeH) + 1 |
| 414 |
|
|
available_NodesInTreeL = NodeToLevel(INODE) |
| 415 |
|
|
NLOW(available_NodesInTreeL) = NLOW(available_NodesInTreeL) + 1 |
| 416 |
|
|
20 CONTINUE |
| 417 |
|
|
MAX1 = 0 |
| 418 |
|
|
MAX2 = 0 |
| 419 |
|
|
/* SET MAX1=LARGEST NEW NUMBER IN NHIGH |
| 420 |
|
|
/* SET MAX2=LARGEST NEW NUMBER IN NLOW |
| 421 |
|
|
for (30 K=1,IDPTH |
| 422 |
|
|
if (2*NACUM(K).EQ.NLOW(K)+NHIGH(K)) GO TO 30 |
| 423 |
|
|
if (NHIGH(K)>MAX1) MAX1 = NHIGH(K) |
| 424 |
|
|
if (NLOW(K)>MAX2) MAX2 = NLOW(K) |
| 425 |
|
|
30 CONTINUE |
| 426 |
|
|
/* SET IT= NUMBER OF LEVEL STRUCTURE TO BE USED |
| 427 |
|
|
IT = 1 |
| 428 |
|
|
if (MAX1>MAX2) IT = 2 |
| 429 |
|
|
if (MAX1.EQ.MAX2) IT = IDFLT |
| 430 |
|
|
if (IT.EQ.2) GO TO 60 |
| 431 |
|
|
if (I.EQ.1) DirectionLargestComponent = -1 |
| 432 |
|
|
/* COPY LevelToNode INTO NodeToLevel FOR EACH NODE IN CONNECTED COMPONENT |
| 433 |
|
|
for (40 K=J,END |
| 434 |
|
|
INODE = ConnectedComponents(K) |
| 435 |
|
|
NodeToLevel(INODE) = LevelToNode(INODE) |
| 436 |
|
|
40 CONTINUE |
| 437 |
|
|
/* UPDATE NACUM TO BE THE SAME AS NHIGH |
| 438 |
|
|
for (50 K=1,IDPTH |
| 439 |
|
|
NACUM(K) = NHIGH(K) |
| 440 |
|
|
50 CONTINUE |
| 441 |
|
|
GO TO 80 |
| 442 |
|
|
/* UPDATE NACUM TO BE THE SAME AS NLOW |
| 443 |
|
|
60 for (70 K=1,IDPTH |
| 444 |
|
|
NACUM(K) = NLOW(K) |
| 445 |
|
|
70 CONTINUE |
| 446 |
|
|
80 CONTINUE |
| 447 |
|
|
RETURN |
| 448 |
|
|
END |
| 449 |
|
|
SUBROUTINE NUMBER(StartNode2, NUM, NDSTK, NodeToLevel, Degree, NewLabel, AssignedLevelST, NUM 10 |
| 450 |
|
|
* LSTPT, NR, Flag, newBandwidth, newProfile, IPFA, DirectionLargestComponent) |
| 451 |
|
|
/* NUMBER PRODUCES THE NUMBERING OF THE GRAPH FOR MIN BANDWIDTH |
| 452 |
|
|
/* StartNode2- ON INPUT THE NODE TO BEGIN NUMBERING ON |
| 453 |
|
|
/* NUM- ON INPUT AND OUTPUT, THE NEXT AVAILABLE NUMBER |
| 454 |
|
|
/* NodeToLevel- THE LEVEL STRUCTURE TO BE USED IN NUMBERING |
| 455 |
|
|
/* NewLabel- THE ARRAY USED TO STORE THE NEW NUMBERING |
| 456 |
|
|
/* AssignedLevelST- ON OUTPUT CONTAINS LEVEL STRUCTURE |
| 457 |
|
|
/* LSTPT[i]- ON OUTPUT, INDEX INTO AssignedLevelST TO FIRST NODE IN ITH AssignedLevel |
| 458 |
|
|
/* LSTPT(I+1) - LSTPT[i] = NUMBER OF NODES IN ITH AssignedLevel |
| 459 |
|
|
/* Flag- =+1 if StartNode2 IS FORWARD END OF PSEUDO-diameter |
| 460 |
|
|
/* =-1 if StartNode2 IS REVERSE END OF PSEUDO-diameter |
| 461 |
|
|
/* newBandwidth- BANDWIDTH OF NEW NUMBERING COMPUTED BY NUMBER |
| 462 |
|
|
/* newProfile- PROFILE OF NEW NUMBERING COMPUTED BY NUMBER |
| 463 |
|
|
/* IPFA- WORKING STORAGE USED TO COMPUTE PROFILE AND BANDWIDTH |
| 464 |
|
|
/* DirectionLargestComponent- INDICATES STEP DIRECTION USED IN NUMBERING(+1 OR -1) |
| 465 |
|
|
/* USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. |
| 466 |
|
|
INTEGER NDSTK |
| 467 |
|
|
INTEGER StartNode2, STKA, STKB, STKC, STKD, XA, XB, ConnectedComponentCounter, XD, CX, END, |
| 468 |
|
|
* NewLabel, TEST |
| 469 |
|
|
COMMON /GRA/ N, IDPTH, ndeg_max |
| 470 |
|
|
/* THE STORAGE IN COMMON BLOCKS CC AND AssignedLevelW IS NOW FREE AND CAN |
| 471 |
|
|
/* BE USED FOR STACKS. |
| 472 |
|
|
COMMON /AssignedLevelW/ STKA(100), STKB(100), STKC(100) |
| 473 |
|
|
COMMON /CC/ STKD(100) |
| 474 |
|
|
DIMENSION IPFA(1) |
| 475 |
|
|
DIMENSION NDSTK(NR,1), NodeToLevel(1), Degree(1), NewLabel(1), AssignedLevelST(1), |
| 476 |
|
|
* LSTPT(1) |
| 477 |
|
|
/* SET UP AssignedLevelST AND LSTPT FROM NodeToLevel |
| 478 |
|
|
for (10 i=0,i<N,++i) |
| 479 |
|
|
IPFA[i] = 0 |
| 480 |
|
|
10 CONTINUE |
| 481 |
|
|
NSTPT = 1 |
| 482 |
|
|
for (30 I=1,IDPTH |
| 483 |
|
|
LSTPT[i] = NSTPT |
| 484 |
|
|
for (20 J=1,N |
| 485 |
|
|
if (NodeToLevel(J)!=I) GO TO 20 |
| 486 |
|
|
AssignedLevelST(NSTPT) = J |
| 487 |
|
|
NSTPT = NSTPT + 1 |
| 488 |
|
|
20 CONTINUE |
| 489 |
|
|
30 CONTINUE |
| 490 |
|
|
LSTPT(IDPTH+1) = NSTPT |
| 491 |
|
|
/* STKA, STKB, STKC AND STKD ARE STACKS WITH POINTERS |
| 492 |
|
|
/* XA,XB,ConnectedComponentCounter, AND XD. CX IS A SPECIAL POINTER INTO STKC WHICH |
| 493 |
|
|
/* INDICATES THE PARTICULAR NODE BEING PROCESSED. |
| 494 |
|
|
/* available_NodesInTree KEEPS TRACK OF THE LEVEL WE ARE WORKING AT. |
| 495 |
|
|
/* INITIALLY STKC CONTAINS ONLY THE INITIAL NODE, StartNode2. |
| 496 |
|
|
available_NodesInTree = 0 |
| 497 |
|
|
if (Flag<0) available_NodesInTree = IDPTH + 1 |
| 498 |
|
|
ConnectedComponentCounter = 1 |
| 499 |
|
|
STKC(ConnectedComponentCounter) = StartNode2 |
| 500 |
|
|
40 CX = 1 |
| 501 |
|
|
XD = 0 |
| 502 |
|
|
available_NodesInTree = available_NodesInTree + Flag |
| 503 |
|
|
LST = LSTPT(available_NodesInTree) |
| 504 |
|
|
LND = LSTPT(available_NodesInTree+1) - 1 |
| 505 |
|
|
/* BEGIN PROCESSING NODE STKC(CX) |
| 506 |
|
|
50 IPRO = STKC(CX) |
| 507 |
|
|
NewLabel(IPRO) = NUM |
| 508 |
|
|
NUM = NUM + DirectionLargestComponent |
| 509 |
|
|
END = Degree(IPRO) |
| 510 |
|
|
XA = 0 |
| 511 |
|
|
XB = 0 |
| 512 |
|
|
/* CHECK ALL ADJACENT NODES |
| 513 |
|
|
for (80 I=1,END |
| 514 |
|
|
TEST = NDSTK(IPRO,I) |
| 515 |
|
|
INX = NewLabel(TEST) |
| 516 |
|
|
/* ONLY NODES NOT NUMBERED OR ALREADY ON A STACK ARE ADDED |
| 517 |
|
|
if (INX.EQ.0) GO TO 60 |
| 518 |
|
|
if (INX<0) GO TO 80 |
| 519 |
|
|
/* for (PRELIMINARY BANDWIDTH AND PROFILE CALCULATIONS |
| 520 |
|
|
NBW = (NewLabel(IPRO)-INX)*DirectionLargestComponent |
| 521 |
|
|
if (DirectionLargestComponent>0) INX = NewLabel(IPRO) |
| 522 |
|
|
if (IPFA(INX)<NBW) IPFA(INX) = NBW |
| 523 |
|
|
GO TO 80 |
| 524 |
|
|
60 NewLabel(TEST) = -1 |
| 525 |
|
|
/* PUT NODES ON SAME LEVEL ON STKA, ALL OTHERS ON STKB |
| 526 |
|
|
if (NodeToLevel(TEST).EQ.NodeToLevel(IPRO)) GO TO 70 |
| 527 |
|
|
XB = XB + 1 |
| 528 |
|
|
STKB(XB) = TEST |
| 529 |
|
|
GO TO 80 |
| 530 |
|
|
70 XA = XA + 1 |
| 531 |
|
|
STKA(XA) = TEST |
| 532 |
|
|
80 CONTINUE |
| 533 |
|
|
/* SORT STKA AND STKB INTO INCREASING DEGREE AND ADD STKA TO STKC |
| 534 |
|
|
/* AND STKB TO STKD |
| 535 |
|
|
if (XA.EQ.0) GO TO 100 |
| 536 |
|
|
if (XA.EQ.1) GO TO 90 |
| 537 |
|
|
CALL SORTDG(STKC, STKA, ConnectedComponentCounter, XA, Degree) |
| 538 |
|
|
GO TO 100 |
| 539 |
|
|
90 ConnectedComponentCounter = ConnectedComponentCounter + 1 |
| 540 |
|
|
STKC(ConnectedComponentCounter) = STKA(XA) |
| 541 |
|
|
100 if (XB.EQ.0) GO TO 120 |
| 542 |
|
|
if (XB.EQ.1) GO TO 110 |
| 543 |
|
|
CALL SORTDG(STKD, STKB, XD, XB, Degree) |
| 544 |
|
|
GO TO 120 |
| 545 |
|
|
110 XD = XD + 1 |
| 546 |
|
|
STKD(XD) = STKB(XB) |
| 547 |
|
|
/* BE SURE TO PROCESS ALL NODES IN STKC |
| 548 |
|
|
120 CX = CX + 1 |
| 549 |
|
|
if (ConnectedComponentCounter>=CX) GO TO 50 |
| 550 |
|
|
/* WHEN STKC IS EXHAUSTED LOOK FOR MIN DEGREE NODE IN SAME LEVEL |
| 551 |
|
|
/* WHICH HAS NOT BEEN PROCESSED |
| 552 |
|
|
MAX = ndeg_max + 1 |
| 553 |
|
|
StartNode2 = N + 1 |
| 554 |
|
|
for (130 I=LST,LND |
| 555 |
|
|
TEST = AssignedLevelST[i] |
| 556 |
|
|
if (NewLabel(TEST)!=0) GO TO 130 |
| 557 |
|
|
if (Degree(TEST)>=MAX) GO TO 130 |
| 558 |
|
|
NewLabel(StartNode2) = 0 |
| 559 |
|
|
NewLabel(TEST) = -1 |
| 560 |
|
|
MAX = Degree(TEST) |
| 561 |
|
|
StartNode2 = TEST |
| 562 |
|
|
130 CONTINUE |
| 563 |
|
|
if (StartNode2.EQ.N+1) GO TO 140 |
| 564 |
|
|
ConnectedComponentCounter = ConnectedComponentCounter + 1 |
| 565 |
|
|
STKC(ConnectedComponentCounter) = StartNode2 |
| 566 |
|
|
GO TO 50 |
| 567 |
|
|
/* if STKD IS EMPTY WE ARE DONE, OTHERWISE COPY STKD ONTO STKC |
| 568 |
|
|
/* AND BEGIN PROCESSING NEW STKC |
| 569 |
|
|
140 if (XD.EQ.0) GO TO 160 |
| 570 |
|
|
for (150 I=1,XD |
| 571 |
|
|
STKC[i] = STKD[i] |
| 572 |
|
|
150 CONTINUE |
| 573 |
|
|
ConnectedComponentCounter = XD |
| 574 |
|
|
GO TO 40 |
| 575 |
|
|
/* for (FINAL BANDWIDTH AND PROFILE CALCULATIONS |
| 576 |
|
|
160 for (170 i=0,i<N,++i) |
| 577 |
|
|
if (IPFA[i]>newBandwidth) newBandwidth = IPFA[i] |
| 578 |
|
|
newProfile = newProfile + IPFA[i] |
| 579 |
|
|
170 CONTINUE |
| 580 |
|
|
RETURN |
| 581 |
|
|
END |
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