1. “Better asymptotics ≠ faster in practice”
Many commenters point out that a lower big‑O does not guarantee a real‑world speed‑up, especially when the new algorithm carries a large constant or only beats the old one on extremely sparse graphs.
“More important is that the new algorithm has a multiplicative factor in m (edges), so it's only efficient for extremely sparse graphs.” – gowld
“If m > n (log n)^{1/3} then this algorithm is slower.” – gowld
“I just don’t see any reason to put it and Dijkstra’s against each other in a head‑to‑head comparison.” – bee_rider
2. “Mathematics is useful only when it can be turned into code”
Engineers emphasize that elegant theory matters only if it translates into implementable solutions; otherwise it is “useless” or merely a warning that perfection is unattainable.
“As an engineer, beautiful mathematics is useless if I can’t convert it to running code.” – yborg
“I find useful mathematics because it tells me that the perfection I have vaguely imagined I could reach for is literally not possible.” – tialaramex
“I read it as a musing on the folly of improvements that don’t deliver benefits within the practical bounds of actual problems.” – shermantanktop
3. “Claims need critical scrutiny and empirical validation”
Several users criticize the article for making grand claims without evidence, for not addressing the central question, or for ignoring the need to test the algorithm in realistic scenarios.
“The paper in question doesn't claim to be practically faster… I struggle to see the point.” – qsort
“He never answered the title of the post (“Faster Than Dijkstra?”).” – WoodenChair
“This was a lot of words that sum up to ‘I heard that new algorithm exists but spent zero effort actually evaluating it.’” – NooneAtAll3
These three themes capture the dominant concerns in the discussion: the gap between theory and practice, the engineer’s view of mathematics, and the insistence on rigorous, evidence‑based evaluation.