Normally a potential y satisfies y_r = 0 and 0 ³ y_w - c_vw -y_v. Given an integer K³0, define a K-potential to be an array y that satisfies yr = 0 and K ³ y_w - c_vw -y_v. Show that for a K-potential y we have that for each node v, yv is within K_n of being the cost of an optimal r-v dipath, i.e. show c(P) + Kn ³ yv for any r to v dipath P in G. HINT: Generalize our proposition from class that said that for a normal potential y, c(P)³yv for any r to v dipath P in G.

 

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