I have the following pseudocode for breadth-first search algorithm

 1 for each vertex uV(G) \ {s}
 2     color[u] = white
 3     d[u] = ∞
 4     π[u] = nil
 5 color[s] = gray
 6 d[s] = 0
 7 π[s] = nil
 8 Q = ∅
 9 Enqueue(Q,s)
10 while q ≠ ∅
11     u = Dequeue(Q)
12     for each vAdj[u]
13         if color[v] == white
14             color[v] = gray
15             d[v] = d[u] + 1
16             π[v] = u
17             Enqueue(Q,v)
18     color[u] = black

Original image

I do not understand what the letter π indicates in this context. I am not familiar with this algorithm and it is a difficult to guess.

I think d indicates the distance, color is of course the color, but that π... it appears to be a variable of some sort but I do not understand its function in this pseudocode.

  • 2
    @Snowman I'd go with the style used in computer science and academic publications rather than math specifically, but I do agree with the general idea. This question is asking about this usage might have been answered by reading the wikipedia page, and π is not something in common use but rather specific to how the author writes the algorithm. I worry that there are far too many variations on pseudocode and asking about what each character in each style means could get out of hand. – user40980 Jun 17 '15 at 1:54
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    Is often the letter π used in pseudocode? Sometimes, but the meaning will vary depending on the context. – Rufflewind Jun 17 '15 at 3:23
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    @Snowman: π here is not a function. It is a mutable array of vertices indexed by vertices. – Rufflewind Jun 17 '15 at 3:26
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    In this context π is just a symbol used in the algorithm, similar to d and color. Sometimes algorithm writers like to use single letter symbols rather than cute names like "parentVertices" or something that might tend to be used in a programming language. – Brandin Jun 17 '15 at 8:13
  • @Snowman Are you joking? It is not a math question. It is about interpreting a pseudocode to write a program, why should this not be about software development, I really cannot understand. – nbro Jun 17 '15 at 9:51

I believe the use of π here is actual “parent of”. So in this case, the “parent” of v  is u because we're looking at all nodes adjacent to u.

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The π vector surely keeps the node u with which you came in node v. This helps when you have to build the BFS tree of the graph. Although it is not necessary, this technique reduces a lot the complexity when you have to perform more time the BFS (ex. the Edmonds–Karp algorithm for computing the maximum flow between two nodes in a graph). In this case you don't have to run the BFS more times as you already have the BFS tree constructed and traverse it from the leaves to the root.

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