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Real funny anileve.
Don't take me for an idiot, please.
R(vi+1) = R(vi) + oei R(di) = R(vi) + jR(vi)ffi|R(di)|k R(di).
The initial value is R(v1) = R(1, 0) = q and R(vi) is integer valued and bounded by zero. Hence, the algorithm terminates after at most log(q) iterations. We obtain that t <= log(q) and that the number of vertices and direction vectors is polynomially bounded in the encoding length of C. This yields an efficient technique to store and to manage the complete basis of C.
Theorem: Let C = cone \Gamma (1, 0), (p, q)\Delta be a 2-dimensional cone defined as above. Then the algorithm constructs in polynomial time vectors v1, . . . , vt+1, d1, . . . , dt and step lengths oe1 . . . , oet and the set
H
Z2(C) :=
t[
i=1 \Phi v
i + oe di : oe = 0, . . . , oei - 1\Psi [ {(p, q)}
is the basis of the cone C.
Overview of the values generated by Algorithm for the cones C1 and C2.
q p i vi R(vi) "i di R(di) oei = j R(v
i)|
R(di)| k
7 4 1 (1, 0) 7 - (0, 1) -4 1
2 (1, 1) 3 1 (1, 2) -1 3 3 (4, 7) 0 - - - -
8 5 1 (1, 0) 8 - (0, 1) -5 1
2 (1, 1) 3 1 (1, 2) -2 1 3 (2, 3) 1 1 (3, 5) -1 1 4 (5, 8) 0 - - - -
I want to thank Dynamic progrmaning @ UofNM for development of the program that let me run the algo.
and give credit to the team that calculated the Johnson Algorithm --a 24 bit encryption algorithm for linking protection.
also from UofNM.
and for your info pasamonster does know
Now i wait for the answer for the problem that you posted.
sorry it took me so long i had to type the whole thing.
Don't take me for an idiot, please.
R(vi+1) = R(vi) + oei R(di) = R(vi) + jR(vi)ffi|R(di)|k R(di).
The initial value is R(v1) = R(1, 0) = q and R(vi) is integer valued and bounded by zero. Hence, the algorithm terminates after at most log(q) iterations. We obtain that t <= log(q) and that the number of vertices and direction vectors is polynomially bounded in the encoding length of C. This yields an efficient technique to store and to manage the complete basis of C.
Theorem: Let C = cone \Gamma (1, 0), (p, q)\Delta be a 2-dimensional cone defined as above. Then the algorithm constructs in polynomial time vectors v1, . . . , vt+1, d1, . . . , dt and step lengths oe1 . . . , oet and the set
H
Z2(C) :=
t[
i=1 \Phi v
i + oe di : oe = 0, . . . , oei - 1\Psi [ {(p, q)}
is the basis of the cone C.
Overview of the values generated by Algorithm for the cones C1 and C2.
q p i vi R(vi) "i di R(di) oei = j R(v
i)|
R(di)| k
7 4 1 (1, 0) 7 - (0, 1) -4 1
2 (1, 1) 3 1 (1, 2) -1 3 3 (4, 7) 0 - - - -
8 5 1 (1, 0) 8 - (0, 1) -5 1
2 (1, 1) 3 1 (1, 2) -2 1 3 (2, 3) 1 1 (3, 5) -1 1 4 (5, 8) 0 - - - -
I want to thank Dynamic progrmaning @ UofNM for development of the program that let me run the algo.
and give credit to the team that calculated the Johnson Algorithm --a 24 bit encryption algorithm for linking protection.
also from UofNM.
and for your info pasamonster does know
Now i wait for the answer for the problem that you posted.
sorry it took me so long i had to type the whole thing.
By the way, "Dynamic Programming" refers to a general class of algorithms where the above fall under (including Johnson's) 
If I remember correctly, Johnson uses a combination of Bellman-Ford and Dijkstra to sove for the shortest paths.
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