() G , N A, . G = {N, A}. A (i, j) N. . . 1.
, - , , . G , N A.
G 1, , G, G; G 1 = {N 1, A 1 } - G = {N, A}, N 1 N A 1 A. , { N } - . - , .
, . d. ( d > 0), ( d < 0) ( d = 0). : N = {N+} {N-} {No}; N+ = {n: dn > 0 }, N- = {n: dn < 0 }, No = {n: dn = 0 }.
, (i, j) , , rij.
F = {fij: (i, j) A} G fij - , :
fij - fji = di, i N; 0 £ fij £ rij. (1)
, . - cij , . :
cij fij opt (2)
(1). ( cij = const), ( cij = F (fkl), (k, l) A) .
.
- , ; , , .
- () .
- ; .
(i, j) i j, i j, , , . : [ i, j ]. (. . 2). , , (. . 2).
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( ) ( ).
[ i, j,..., k ] i k G 1 G, , ( i k) . .
(i, j,..., k) i k G 2 G, , ( i k) G 2 G 2.
- .
- .
- .
, - .
, .
, .
. 3 (), () () (); (, ), (, ) (); () (); (, , , ) (, ) .
C - , G G1, G2 . :
C = {(i, j): (i, j) A}:
G = G 1 G 2 C; G 1 G 2 = , G 1 C = , G 2 C = ; i, j G: i G 1, j G 2; (i, j) C.
C, Rc (G 1 G 2 ) G 1 G 2- rij [ i, j ] C, G 1 G 2:
Rc (G 1 G2) = rij.
, : Rc (G 1 G 2 ) Rc (G 2 G 1 ). s r , , . s G 1, r G 2; Rc (s r) = Rc. . , , , , - .
.
G 1 G, G, .
, :
1. .
2. .
3. .
. () , . , G o = {N, Ao} - G = {N, A}, A oc A G o - .
, cij, ij .
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, - , .
- , .
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, , , . 5.