# Bellman-Ford algorithm from Éva Tardos

I am trying to understand the Bellman-Ford algorithm from Jon Kleinberg, Éva Tardos: *[Algorithm Design]. Page no: 296 The recursive equation that is written: $$M[v]= \min(M[v], \min_{w\in V} (c_{vw} + M[w]).$$

I am not getting how this equation is correct?
Because in the book it is written that $$M[v]$$ is the shortest path from $$v-t$$,
but shouldn't $$M[v]$$ be the shortest path from $$s-v$$ using at most $$i-1$$ edges?

• Welcome to COMPUTER SCIENCE @SE. When something in a book seems off, restart reading at the start of the paragraph, sub-chapter or chapter. In 6.8 Shortest Paths in a Graph, there's a note starting Let’s use OPT(i, v) to denote the minimum… following the first proof. Also, look at the "dynamic programming table in (b)" two pages before the formula. – greybeard Oct 24 at 6:58
• (While you're at it: I seem to have missed a closing parenthesis, and there is one "italics star" left from removing the URL.) – greybeard Oct 25 at 16:56