Re: An added line to Tarjan's SCC algorithm in Muchnik's Advanced Compiler Design

woong.jun@gmail.com
Fri, 24 Aug 2018 00:40:12 -0700 (PDT)

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From: woong.jun@gmail.com
Newsgroups: comp.compilers
Date: Fri, 24 Aug 2018 00:40:12 -0700 (PDT)
Organization: Compilers Central
References: 18-08-001 18-08-003
Keywords: optimize, analysis, books
In-Reply-To: 18-08-003

David Lovemore wrote:
> On Thursday, August 16, 2018 at 1:41:12 PM UTC+1, woon...@gmail.com wrote:
> > The official errata for the book, Advanced Compiler Design and Implementation
> > by Steven Muchnik added, among other fixes, this line to the Tarjan's algorithm
> > to find maximal strongly connected components (SCCs) from a directed graph.
> >
> > All_SCC U= {{Stack[1]}}
> >
> > where I replaced with brackets an arrow to mean retrival of an element from a
> > sequence named Stack. ...
>
>
> I don't have the book, so I can't see implementation of
> Strong_Components.


Strong_Components implements an algorithm essentially same to what
Tarjan's original paper specifies.


Strong_Components looks like this:


        x is a parameter to denote a flowgraph node


        LowLink(x) = Dfn(x) = NextDfn += 1
        push x to Stack
        for each y from x's successors do
                if Dfn(y) = 0 then
                        Strong_Components(y)
                        LowLink(x) = min(LowLink(x), LowLink(y))
                elif Dfn(y) < Dfn(x) and y is on Stack then
                        LowLink(x) = min(LowLink(x), Dfn(y))
                fi
        od
        if LowLink(x) = Dfn(x) then // x is root of SCC
                SCC is an empty set
                while Stack is not empty do
                        z = top from Stack without popping
                        if Dfn(z) < Dfn(x) then
                                add set SCC to another set All_SCC
                                return
                        fi
                        pop from Stack
                        add z to SCC
                od
                add set SCC to set All_SCC
        fi


> But I believe the description of the algorithm on
> wikipedia is correct. I suggest comparing with that.
>
> https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm


Thanks for the reference. I compared and found no differences.


If the line in question had come from the text instead of the errata,
I would not have posted this question. I still wonder why the author
decided to add the line that looks unnecessary.


Thanks.




--
Woong Jun (woong.jun at gmail.com)
http://code.woong.org


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