Does anyone know what the subscript before the function means? $$ _pf_p $$

It's part of a definition for selfish routing in networks:

Let $N = (V,E)$ be the network, which is a directed graph. There are $k$ source-destination paris $\{{s_1}, {t_1}\}, ..., \{{s_k}, {t_k}\}$. ${P_i}$ = the set of paths from ${s_i}$ to ${t_i}$ and $P = \cup_iP_i$. The flow $f: P \rightarrow R^+$, where $P$ is negligible traffic and $R^+$ represents a flow. The load of edge $e$ is $f_e = \sum_{p\in P}$ such that $e$ is in $_pf_p$.

Also, am I right in thinking this means the union of all possible paths? $$P = \cup_iP_i$$


  • $\begingroup$ should this be migrated to Computer Science. I might be wrong. $\endgroup$ – Guy Mar 4 '14 at 13:33
  • $\begingroup$ This is not a standard notation. Where did you see it? The book or article should explain what the notation means. @Sabyasachi It could be a Computer Science question, except that since this isn't a standard notation, we can't help much more than here. CS would be a better place than here to come up with a correct defintion of the load of an edge. $\endgroup$ – Gilles 'SO- stop being evil' Mar 4 '14 at 13:42
  • $\begingroup$ @Gilles so should it be migrated or not? $\endgroup$ – Guy Mar 4 '14 at 13:44
  • $\begingroup$ @Sabyasachi The question can be migrated, but: tearfulheart, you should say where you found this definition. $\endgroup$ – Gilles 'SO- stop being evil' Mar 4 '14 at 13:51
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    $\begingroup$ (If you chose to follow my advice above, use the following code for the "correct" typesetting: $f_e = \sum_{p\in P \text{ such that }e\text{ is in }p} f_p$.) $\endgroup$ – Willie Wong Mar 5 '14 at 9:14

"The load of edge $e$ is $f_e = \sum_{p\in P}$ such that $e$ is in $_pf_p$" should be: $$f_e = \sum_{p\in P \text{ such that }e\text{ is in }p} f_p$$


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