Patent ID: 11954061
Assignee: BEIJING TSINGMICRO INTELLIGENT TECHNOLOGY CO., LTD.
Field: Computer technology (Electrical engineering)
Classification: CPC G | IPC G

Claim 4:
5. The mapping method for the reconfigurable array according to claim 4, wherein S57 is performed by a formula (9):, V
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                
                  
                
                ⁢
                
                  M
                  ⁡
                  
                    (
                    
                      i
                      ,
                      
                        
                          T
                          ⁢
                          
                            
                          
                          ⁢
                          S
                          *
                          P
                          ⁢
                          
                            
                          
                          ⁢
                          E
                          ⁢
                          
                            
                          
                          ⁢
                          _
                          ⁢
                          
                            
                          
                          ⁢
                          num
                        
                        +
                        j
                      
                    
                    )
                  
                
              
              ≤
              
                
                  ∑
                  
                    b
                    ∈
                    
                      L
                      ⁢
                      
                        
                      
                      ⁢
                      _
                      ⁢
                      
                        
                      
                      ⁢
                      num
                    
                  
                
                ⁢
                
                  E
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    ⁡
                    
                      (
                      
                        a
                        ,
                        
                          
                            
                              (
                              
                                
                                  T
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  S
                                
                                ⁢
                                
                                  
                                
                                +
                                1
                              
                              )
                            
                            ⁢
                            
                              
                            
                            ⁢
                            %
                            ⁢
                            
                              
                            
                            ⁢
                            T
                            ⁢
                            
                              
                            
                            ⁢
                            S
                            ⁢
                            
                              
                            
                            ⁢
                            _
                            ⁢
                            
                              
                            
                            ⁢
                            max
                            *
                            L
                            ⁢
                            
                              
                            
                            ⁢
                            _
                            ⁢
                            
                              
                            
                            ⁢
                            num
                          
                          +
                          b
                        
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  where
                  ⁢
                  
                    
                  
                  ⁢
                  n
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      l
                      ⁡
                      
                        [
                        j
                        ]
                      
                    
                    ⁡
                    
                      [
                      b
                      ]
                    
                  
                
              
            
            ⁢
            
              
            
            &
          
          ⁢
          intra
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          dep
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          
            edge
            ⁡
            
              [
              a
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            ∀
            
              a
              ∈
              E
            
          
        
        ,
        
          ∀
          
            
              T
              ⁢
              
                
              
              ⁢
              S
            
            ∈
            
              TS
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              max
            
          
        
        ,
        
          ∀
          
            j
            ∈
            
              PE
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
        
        ,
        
          
        
        ⁢
        
          ∀
          
            i
            ∈
            V
          
        
        ,
      
    
    
      
        (
        9
        )
      
    
  

where intra_dep_edge[ ] represents an edge that is a dependence within a cycle in the data dependence graph;
wherein S58 is performed by a formula (10):, V2M
                    ⁡
                    
                      (
                      
                        i
                        ,
                        
                          
                            TS
                            *
                            PE
                            ⁢
                            
                              
                            
                            ⁢
                            _
                            ⁢
                            
                              
                            
                            ⁢
                            num
                          
                          +
                          j
                        
                      
                      )
                    
                  
                  ≤
                  
                    
                      ∑
                      
                        b
                        ∈
                        
                          L
                          ⁢
                          _
                          ⁢
                          num
                        
                      
                      
                        
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      E
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        ⁡
                        
                          (
                          
                            a
                            ,
                            
                              
                                T
                                ⁢
                                
                                  
                                
                                ⁢
                                S
                                *
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                              +
                              b
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      where
                      ⁢
                      
                        
                      
                      ⁢
                      l
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          n
                          ⁡
                          
                            [
                            j
                            ]
                          
                        
                        ⁡
                        
                          [
                          b
                          ]
                        
                      
                    
                  
                
                ⁢
                
                  
                
                &
              
              ⁢
              
                
                  G
                  ⁡
                  
                    [
                    
                      a
                      +
                      V
                    
                    ]
                  
                
                ⁡
                
                  [
                  i
                  ]
                
              
            
            &
          
          ⁢
          intra
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          dep
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          
            edge
            ⁡
            
              [
              a
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            ∀
            
              a
              ∈
              E
            
          
        
        ,
        
          ∀
          
            
              T
              ⁢
              
                
              
              ⁢
              S
            
            ∈
            
              T
              ⁢
              
                
              
              ⁢
              S
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              max
            
          
        
        ,
        
          ∀
          
            j
            ∈
            
              P
              ⁢
              
                
              
              ⁢
              E
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
        
        ,
        
          
        
        ⁢
        
          ∀
          
            i
            ∈
            V
          
        
        ,
      
    
    
      
        (
        10
        )
      
    
  

where TS represents a time step at which the processing vertex in the data dependence graph is executed, and intra_dep_edge[ ] represents an edge that is a dependence within a cycle in the data dependence graph;
wherein S59 is performed by a formula (11):, V
          ⁢
          
            
          
          ⁢
          2
          ⁢
          
            
          
          ⁢
          
            M
            ⁡
            
              (
              
                i
                ,
                
                  
                    ii
                    *
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    E
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    num
                  
                  +
                  j
                
              
              )
            
          
        
        ≤
        
           
          
            
              ∑
              
                
                  
                    
                      
                        b
                        ∈
                        
                          L
                          ⁢
                          _
                          ⁢
                          num
                        
                      
                      ,
                    
                  
                
                
                  
                    
                      if
                      ⁢
                      
                        
                      
                      ⁢
                      n
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          l
                          ⁡
                          
                            [
                            j
                            ]
                          
                        
                        ⁡
                        
                          [
                          b
                          ]
                        
                      
                    
                  
                
              
              
                
              
            
            ⁢
            
              
            
            ⁢
            
              E
              ⁢
              
                
              
              ⁢
              2
              ⁢
              
                
              
              ⁢
              L
              ⁢
              
                 
                
                  
                    
                      
                        
                          (
                          
                            a
                            ,
                            
                              
                                
                                  (
                                  
                                    ii
                                    +
                                    1
                                  
                                  )
                                
                                ⁢
                                
                                  
                                
                                ⁢
                                %
                                ⁢
                                
                                  
                                
                                ⁢
                                II
                                *
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                              +
                              b
                            
                          
                          )
                        
                        ⁢
                        
                          
                        
                        ⁢
                        where
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        
                          
                            l
                            ⁡
                            
                              [
                              j
                              ]
                            
                          
                          ⁡
                          
                            [
                            b
                            ]
                          
                        
                      
                      ⁢
                      
                        
                      
                      &
                    
                    ⁢
                    inner
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    dep
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    
                      edge
                      ⁡
                      
                        [
                        a
                        ]
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      ∀
                      
                        a
                        ∈
                        E
                      
                    
                  
                  ,
                  
                    ∀
                    
                      j
                      ∈
                      
                        P
                        ⁢
                        
                          
                        
                        ⁢
                        E
                        ⁢
                        
                          
                        
                        ⁢
                        _
                        ⁢
                        
                          
                        
                        ⁢
                        num
                      
                    
                  
                  ,
                  
                    ∀
                    
                      ii
                      ∈
                      II
                    
                  
                  ,
                  
                    ∀
                    
                      i
                      ∈
                      V
                    
                  
                  ,
                
              
            
          
        
      
    
    
      
        (
        11
        )
      
    
  

where n2l[ ][ ] represents the first adjacency matrix for indicating a connection relationship between the processing element and the output link of the reconfigurable architecture, G[ ][ ] represents an adjacency matrix for indicating a connection relationship between the processing vertex and the edge in the data dependence graph, and inner_dep_edge[ ] represents an edge that is a dependence across different cycles in the data dependence graph;
wherein S510 is performed by a formula (12):, V
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      M
                      ⁡
                      
                        (
                        
                          i
                          ,
                          
                            
                              ii
                              *
                              P
                              ⁢
                              
                                
                              
                              ⁢
                              E
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              num
                            
                            +
                            j
                          
                        
                        )
                      
                    
                  
                  ≤
                  
                    
                      ∑
                      
                        
                          
                            
                              
                                b
                                ∈
                                
                                  L
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  _
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  num
                                
                              
                              ,
                            
                          
                        
                        
                          
                            
                              if
                              ⁢
                              
                                
                              
                              ⁢
                              l
                              ⁢
                              
                                
                              
                              ⁢
                              2
                              ⁢
                              
                                
                              
                              ⁢
                              
                                
                                  n
                                  ⁡
                                  
                                    [
                                    j
                                    ]
                                  
                                
                                ⁡
                                
                                  [
                                  b
                                  ]
                                
                              
                            
                          
                        
                      
                      
                        
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      E
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        ⁡
                        
                          (
                          
                            a
                            ,
                            
                              
                                ii
                                *
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                              +
                              b
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      where
                      ⁢
                      
                        
                      
                      ⁢
                      l
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          n
                          ⁡
                          
                            [
                            j
                            ]
                          
                        
                        ⁡
                        
                          [
                          b
                          ]
                        
                      
                    
                  
                
                ⁢
                
                  
                
                &
              
              ⁢
              
                
                  G
                  ⁡
                  
                    [
                    
                      a
                      +
                      V
                    
                    ]
                  
                
                ⁡
                
                  [
                  i
                  ]
                
              
            
            &
          
          ⁢
          inner
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          dep
          ⁢
          
            
          
          ⁢
          _
          ⁢
          
            
          
          ⁢
          
            edge
            ⁡
            
              [
              a
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            ∀
            
              a
              ∈
              E
            
          
        
        ,
        
          ∀
          
            j
            ∈
            
              PE
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
        
        ,
        
          ∀
          
            ii
            ∈
            II
          
        
        ,
        
          ∀
          
            i
            ∈
            V
          
        
        ,
      
    
    
      
        (
        12
        )
      
    
  

where l2n[ ][ ] represents the second adjacency matrix for indicating a connection relationship between the input link and the processing element of the reconfigurable architecture;
wherein S511 is performed by a formula (13):, ∑
                  
                    
                      
                        
                          
                            b
                            ∈
                            
                              L
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              num
                            
                          
                          ,
                        
                      
                    
                    
                      
                        
                          if
                          ⁢
                          
                            
                          
                          ⁢
                          l
                          ⁢
                          
                            
                          
                          ⁢
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          
                            
                              n
                              ⁡
                              
                                [
                                j
                                ]
                              
                            
                            ⁡
                            
                              [
                              b
                              ]
                            
                          
                        
                      
                    
                  
                  
                    
                  
                
                ⁢
                
                  
                
                ⁢
                
                  E
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    ⁡
                    
                      (
                      
                        a
                        ,
                        
                          
                            TS
                            *
                            
                              L
                              num
                            
                          
                          +
                          b
                        
                      
                      )
                    
                  
                
              
              ≤
              
                
                  V
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    M
                    ⁡
                    
                      (
                      
                        i
                        ,
                        
                          
                            T
                            ⁢
                            
                              
                            
                            ⁢
                            S
                            *
                            P
                            ⁢
                            
                              
                            
                            ⁢
                            
                              E
                              num
                            
                          
                          +
                          j
                        
                      
                      )
                    
                  
                
                +
                
                  
                    ∑
                    
                      
                        
                          
                            
                              c
                              ∈
                              
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                            
                            ,
                          
                        
                      
                      
                        
                          
                            if
                            ⁢
                            
                              
                            
                            ⁢
                            l
                            ⁢
                            
                              
                            
                            ⁢
                            2
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  [
                                  j
                                  ]
                                
                              
                              ⁡
                              
                                [
                                c
                                ]
                              
                            
                          
                        
                      
                    
                    
                      
                    
                  
                  ⁢
                  
                    E
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      ⁡
                      
                        (
                        
                          a
                          ,
                          
                            
                              
                                (
                                
                                  
                                    T
                                    ⁢
                                    
                                      
                                    
                                    ⁢
                                    S
                                  
                                  +
                                  1
                                
                                )
                              
                              ⁢
                              
                                
                              
                              ⁢
                              %
                              ⁢
                              
                                
                              
                              ⁢
                              T
                              ⁢
                              
                                
                              
                              ⁢
                              S
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              max
                              *
                              L
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              num
                            
                            +
                            c
                          
                        
                        )
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    where
                    ⁢
                    
                      
                    
                    ⁢
                    intra
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    dep
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    
                      edge
                      ⁡
                      
                        [
                        a
                        ]
                      
                    
                  
                
              
            
            ⁢
            
              
            
            &
          
          ⁢
          
            
          
          ⁢
          
            
              graph
              ⁡
              
                [
                
                  a
                  +
                  V
                
                ]
              
            
            ⁡
            
              [
              i
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            ∀
            
              a
              ∈
              E
            
          
        
        ,
        
          j
          ⁢
          
            ∀
            
              P
              ⁢
              
                
              
              ⁢
              E
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
        
        ,
        
          TS
          ∈
          
            TS
            ⁢
            
              
            
            ⁢
            _
            ⁢
            
              
            
            ⁢
            max
          
        
        ,
        
          ∀
          
            i
            ∈
            V
          
        
        ,
      
    
    
      
        (
        13
        )
      
    
  

where intra_dep_edge[ ] represents an edge that is a dependence within a cycle in the data dependence graph;
wherein S512 is performed by a formula (14):, ∑
                  
                    
                      
                        
                          
                            b
                            ∈
                            
                              L
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              num
                            
                          
                          ,
                        
                      
                    
                    
                      
                        
                          if
                          ⁢
                          
                            
                          
                          ⁢
                          l
                          ⁢
                          
                            
                          
                          ⁢
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          
                            
                              n
                              ⁡
                              
                                [
                                j
                                ]
                              
                            
                            ⁡
                            
                              [
                              b
                              ]
                            
                          
                        
                      
                    
                  
                  
                    
                  
                
                ⁢
                
                  E
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    ⁡
                    
                      (
                      
                        a
                        ,
                        
                          
                            
                              (
                              
                                
                                  T
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  S
                                
                                +
                                1
                              
                              )
                            
                            ⁢
                            
                              
                            
                            ⁢
                            %
                            ⁢
                            
                              
                            
                            ⁢
                            T
                            ⁢
                            
                              
                            
                            ⁢
                            S
                            ⁢
                            
                              
                            
                            ⁢
                            _
                            ⁢
                            
                              
                            
                            ⁢
                            max
                            *
                            L
                            ⁢
                            
                              
                            
                            ⁢
                            _
                            ⁢
                            
                              
                            
                            ⁢
                            num
                          
                          +
                          b
                        
                      
                      )
                    
                  
                
              
              ≤
              
                
                  V
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  
                    M
                    ⁡
                    
                      (
                      
                        i
                        ,
                        
                          
                            T
                            ⁢
                            
                              
                            
                            ⁢
                            S
                            *
                            P
                            ⁢
                            
                              
                            
                            ⁢
                            
                              E
                              num
                            
                          
                          +
                          j
                        
                      
                      )
                    
                  
                
                +
                
                  
                    ∑
                    
                      
                        
                          
                            
                              c
                              ∈
                              
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                            
                            ,
                          
                        
                      
                      
                        
                          
                            if
                            ⁢
                            
                              
                            
                            ⁢
                            l
                            ⁢
                            
                              
                            
                            ⁢
                            2
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  [
                                  j
                                  ]
                                
                              
                              ⁡
                              
                                [
                                c
                                ]
                              
                            
                          
                        
                      
                    
                    
                      
                    
                  
                  ⁢
                  
                    E
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      ⁡
                      
                        (
                        
                          a
                          ,
                          
                            
                              T
                              ⁢
                              
                                
                              
                              ⁢
                              S
                              *
                              L
                              ⁢
                              
                                
                              
                              ⁢
                              _
                              ⁢
                              
                                
                              
                              ⁢
                              num
                            
                            +
                            c
                          
                        
                        )
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    where
                    ⁢
                    
                      
                    
                    ⁢
                    intra
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    dep
                    ⁢
                    
                      
                    
                    ⁢
                    _
                    ⁢
                    
                      
                    
                    ⁢
                    
                      edge
                      ⁡
                      
                        [
                        a
                        ]
                      
                    
                  
                
              
            
            ⁢
            
              
            
            &
          
          ⁢
          
            
          
          ⁢
          
            
              graph
              ⁢
              
                
              
              [
              i
              ]
            
            ⁡
            
              [
              
                a
                +
                V
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            ∀
            
              a
              ∈
              E
            
          
        
        ,
        
          j
          ∈
          
            P
            ⁢
            
              
            
            ⁢
            E
            ⁢
            
              
            
            ⁢
            _
            ⁢
            
              
            
            ⁢
            num
          
        
        ,
        
          ii
          ∈
          II
        
        ,
        
          
        
        ⁢
        
          
            i
            ∈
            
              
            
            ⁢
            V
          
          ;
        
      
    
    
      
        (
        l4
        )
      
    
  

wherein S513 is performed by a formula (15):, ⁢
        
          
            
              
                
                  
                    ∑
                    
                      
                        
                          
                            
                              b
                              ∈
                              
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                            
                            ,
                          
                        
                      
                      
                        
                          
                            if
                            ⁢
                            
                              
                            
                            ⁢
                            l
                            ⁢
                            
                              
                            
                            ⁢
                            2
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  [
                                  j
                                  ]
                                
                              
                              ⁡
                              
                                [
                                b
                                ]
                              
                            
                          
                        
                      
                    
                    
                      
                    
                  
                  ⁢
                  
                    E
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      ⁡
                      
                        (
                        
                          a
                          ,
                          
                            
                              ii
                              *
                              
                                L
                                num
                              
                            
                            +
                            b
                          
                        
                        )
                      
                    
                  
                
                ≤
                
                  
                    V
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      M
                      ⁡
                      
                        (
                        
                          i
                          ,
                          
                            
                              ii
                              *
                              P
                              ⁢
                              
                                
                              
                              ⁢
                              
                                E
                                num
                              
                            
                            +
                            j
                          
                        
                        )
                      
                    
                  
                  +
                  
                    
                      ∑
                      
                        
                          
                            
                              
                                c
                                ∈
                                
                                  L
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  _
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  num
                                
                              
                              ,
                            
                          
                        
                        
                          
                            
                              if
                              ⁢
                              
                                
                              
                              ⁢
                              l
                              ⁢
                              
                                
                              
                              ⁢
                              2
                              ⁢
                              
                                
                              
                              ⁢
                              
                                
                                  n
                                  ⁡
                                  
                                    [
                                    j
                                    ]
                                  
                                
                                ⁡
                                
                                  [
                                  c
                                  ]
                                
                              
                            
                          
                        
                      
                      
                        
                      
                    
                    ⁢
                    
                      E
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        ⁡
                        
                          (
                          
                            a
                            ,
                            
                              
                                
                                  (
                                  
                                    ii
                                    +
                                    1
                                  
                                  )
                                
                                ⁢
                                
                                  
                                
                                ⁢
                                %
                                ⁢
                                
                                  
                                
                                ⁢
                                II
                                *
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                              +
                              c
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      where
                      ⁢
                      
                        
                      
                      ⁢
                      inner
                      ⁢
                      
                        
                      
                      ⁢
                      _
                      ⁢
                      
                        
                      
                      ⁢
                      dep
                      ⁢
                      
                        
                      
                      ⁢
                      _
                      ⁢
                      
                        
                      
                      ⁢
                      
                        edge
                        ⁡
                        
                          [
                          a
                          ]
                        
                      
                    
                  
                
              
              ⁢
              
                
              
              &
            
            ⁢
            
              
            
            ⁢
            
              
                graph
                ⁢
                
                  
                
                [
                
                  a
                  +
                  V
                
                ]
              
              ⁡
              
                [
                i
                ]
              
            
            ⁢
            
              
            
            ⁢
            
              ∀
              
                a
                ∈
                E
              
            
          
          ,
          
            j
            ∈
            
              P
              ⁢
              
                
              
              ⁢
              E
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
          ,
          
            ii
            ∈
            II
          
          ,
          
            
              i
              ∈
              
                
              
              ⁢
              V
            
            ;
          
        
      
    
    
      
        (
        15
        )
      
    
  

and
wherein S514 is performed by a formula (16):, ⁢
        
          
            
              
                
                  
                    ∑
                    
                      
                        
                          
                            
                              b
                              ∈
                              
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                            
                            ,
                          
                        
                      
                      
                        
                          
                            if
                            ⁢
                            
                              
                            
                            ⁢
                            l
                            ⁢
                            
                              
                            
                            ⁢
                            2
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  [
                                  j
                                  ]
                                
                              
                              ⁡
                              
                                [
                                b
                                ]
                              
                            
                          
                        
                      
                    
                    
                      
                    
                  
                  ⁢
                  
                    E
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      ⁡
                      
                        (
                        
                          a
                          ,
                          
                            
                              
                                (
                                
                                  ii
                                  +
                                  1
                                
                                )
                              
                              ⁢
                              
                                
                              
                              ⁢
                              %
                              ⁢
                              
                                
                              
                              ⁢
                              II
                              *
                              
                                L
                                num
                              
                            
                            +
                            b
                          
                        
                        )
                      
                    
                  
                
                ⁢
                
                  
                
                ≤
                
                  
                    V
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    M
                    ⁢
                    
                      (
                      
                        i
                        ,
                        
                          
                            ii
                            *
                            P
                            ⁢
                            
                              
                            
                            ⁢
                            
                              E
                              num
                            
                          
                          +
                          j
                        
                      
                      )
                    
                  
                  +
                  
                    
                      ∑
                      
                        
                          
                            
                              
                                c
                                ∈
                                
                                  L
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  _
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  num
                                
                              
                              ,
                            
                          
                        
                        
                          
                            
                              if
                              ⁢
                              
                                
                              
                              ⁢
                              l
                              ⁢
                              
                                
                              
                              ⁢
                              2
                              ⁢
                              
                                
                              
                              ⁢
                              
                                
                                  n
                                  ⁡
                                  
                                    [
                                    j
                                    ]
                                  
                                
                                ⁡
                                
                                  [
                                  c
                                  ]
                                
                              
                            
                          
                        
                      
                      
                        
                      
                    
                    ⁢
                    
                      E
                      ⁢
                      
                        
                      
                      ⁢
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        ⁡
                        
                          (
                          
                            a
                            ,
                            
                              
                                ii
                                *
                                L
                                ⁢
                                
                                  
                                
                                ⁢
                                _
                                ⁢
                                
                                  
                                
                                ⁢
                                num
                              
                              +
                              c
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      where
                      ⁢
                      
                        
                      
                      ⁢
                      inner
                      ⁢
                      
                        
                      
                      ⁢
                      _
                      ⁢
                      
                        
                      
                      ⁢
                      dep
                      ⁢
                      
                        
                      
                      ⁢
                      _
                      ⁢
                      
                        
                      
                      ⁢
                      
                        edge
                        ⁡
                        
                          [
                          a
                          ]
                        
                      
                    
                  
                
              
              ⁢
              
                
              
              &
            
            ⁢
            
              
            
            ⁢
            
              
                graph
                ⁢
                
                  
                
                [
                i
                ]
              
              ⁡
              
                [
                
                  a
                  +
                  V
                
                ]
              
            
            ⁢
            
              
            
            ⁢
            
              ∀
              
                a
                ∈
                E
              
            
          
          ,
          
            j
            ∈
            
              P
              ⁢
              
                
              
              ⁢
              E
              ⁢
              
                
              
              ⁢
              _
              ⁢
              
                
              
              ⁢
              num
            
          
          ,
          
            ii
            ∈
            II
          
          ,
          
            i
            ∈
            
              
            
            ⁢
            
              V
              .
            
          
        
      
    
    
      
        (
        16
        )