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From: David Abrahams (david.abrahams_at_[hidden])
Date: 20020115 13:35:08
Oh whoops:
> DIJKSTRA(G, s, w)
> for each vertex u in V
> d[u] := infinity
> p[u] := u
> end for
> INSERT(Q, (s,s,0))
> while (Q != Ã˜)
> u,t,x := EXTRACTMIN(Q)
^^^^^
> if u not in S
> d[u] = x // optional! d not needed for algorithm
> p[u] = t // also optional
> S := S U { u }
> for each vertex v in Adj[u]
> if v not in S // optimization  first path to v is always shortest
> INSERT(Q, (u, v, x + w(u,v))) // put the path in the queue
> end for
> end while
that should have been t,u,x
Dave
 Original Message 
From: "David Abrahams" <david.abrahams_at_[hidden]>
To: <boost_at_[hidden]>
Cc: "Jeremy Siek" <jsiek_at_[hidden]>; "LieQuan Lee" <llee_at_[hidden]>
Sent: Tuesday, January 15, 2002 1:17 PM
Subject: Re: [boost] BGL: dijkstra questions
> Here I go, sticking my foot in my mouth... Maybe you can come up with a
> simple counterexample for me?
>
> I can't make this algorithm break (in my head).
>
> Further, by "the optimization" I assume you mean the line labelled "//
> optimization", yes? I don't see how that breaks anything, but even if we
> leave that out, I think all of the advantages remain.
>
>  Original Message 
> From: "LieQuan Lee" <llee_at_[hidden]>
> To: <boost_at_[hidden]>
> Sent: Tuesday, January 15, 2002 12:58 PM
> Subject: Re: [boost] BGL: dijkstra questions
>
>
>
> On Tue, 20020115 at 12:34, David Abrahams wrote:
> > I know this will seem like a silly question to some; so much the better,
> the
> > answer should be easy:
> >
> > I don't understand the reason for the decreasekey operation. I mean, I
> > understand why it's needed the way that the algorithm is formulated, but
> > AFAIK a formulation which stores the current weight of any path in the
> queue
> > is far, far simpler and does the job:
> >
> > DIJKSTRA(G, s, w)
> > for each vertex u in V
> > d[u] := infinity
> > p[u] := u
> > end for
> > INSERT(Q, (s,s,0))
> > while (Q != Ã˜)
> > u,t,x := EXTRACTMIN(Q)
> > if u not in S
> > d[u] = x // optional! d not needed for algorithm
> > p[u] = t // also optional
> > S := S U { u }
> > for each vertex v in Adj[u]
> > if v not in S // optimization  first path to v is always
shortest
> > INSERT(Q, (u, v, x + w(u,v))) // put the path in the queue
> > end for
> > end while
>
> That algorithm yeilds a shortestpath *only* when the weight of all
> edges is the same. The optimization is wrong when edges have different
> weight.
>
> 
> LieQuan Lee (AKA: Rich Lee)
> Research Associate
> Open Systems Laboratory Phone: 18128553608
> Computer Science Department Email: llee_at_[hidden]
> Indiana University Homepage: http://www.osl.iu.edu/~llee
>
>
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