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Mar 30, 2017 at 11:04 comment added xavierm02 @TienanhNguyen No. If you get the shortest path using $w'$, you may not get a shortest path for $w$ because of the length problem. And if you always keep track of the length and then use $w'(p)-|p|W$ whenever you compare, then you're just using $w$ which can have negative edges so Dijkstra may not work.
Mar 29, 2017 at 18:11 comment added Tienanh Nguyen But does the algorithm I mentioned above correct? Since Johnson a lot more complicated, I highly doubted that the algorithm above can do the same things as Johnson with less complexity.
Mar 29, 2017 at 15:38 history edited xavierm02 CC BY-SA 3.0
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Mar 29, 2017 at 15:31 history edited xavierm02 CC BY-SA 3.0
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Mar 29, 2017 at 15:20 history answered xavierm02 CC BY-SA 3.0