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Explain the limitation of Dijkstra’s algorithm

#1
12-21-2025, 04:58 AM
You see the main issue with this approach right away. It only handles positive distances between points. Negative values throw everything off completely. I have watched it fail in real setups. You end up with wrong paths that make no sense.

Perhaps the algorithm assumes all connections stay above zero. But life throws curveballs with minus signs everywhere. I tried it once on a graph with a single dip. Results came out twisted and useless. You cannot trust the output after that.

Now think about cycles that pull numbers lower. The method never checks for those loops. It just keeps pushing forward without care. I notice this creates infinite problems in practice. You might chase shorter routes that loop forever.

Also the speed drops fast on crowded networks. Dense connections slow the whole process down. I prefer faster options when graphs grow big. You lose time waiting for answers that drag. Or maybe you switch methods early to avoid hassle.

Then there is the single starting point limit. It never covers every pair at once. I find this restrictive for full maps. You need extra runs to fill gaps. Perhaps other tools handle multiple starts better.

But the greedy choice locks in early decisions. Later fixes become impossible without restarts. I see this waste effort on large tasks. You end up recalculating from scratch often. Now imagine scaling this to city wide routes.

The non negative rule blocks many real models. Weights from costs or times can dip below. I avoid it when data includes penalties. You risk bad planning if edges turn sour. Or perhaps adjust inputs first but that adds work.

Also memory use climbs with bigger structures. Priority queues eat space quickly here. I track usage in my own tests. You might hit walls on standard machines. Then performance tanks without warning signs.

Perhaps updates in variants fix some spots. Yet core flaws stay put in basics. I stick to warnings for juniors like you. You learn to pick tools that match data. Now negative cycles demand different handling altogether.

The method skips detection steps entirely. It assumes clean positive flows only. I caught errors in test cases with loops. You see shortest paths vanish into nothing. But real networks have such traps hidden.

Efficiency suffers without fancy heaps sometimes. Basic versions crawl on complex inputs. I switched to better heaps in projects. You gain speed yet limits remain the same. Or maybe test small first before full runs.

You notice it ignores dynamic changes too. Graphs that shift mid process break it. I dealt with live updates in work. You cannot rerun everything each time. Perhaps batch changes but that delays results.

Then the assumption of static weights hurts. Costs change in actual scenarios often. I plan around this by choosing flexible code. You save headaches with alternatives ready. Now graduate work shows these gaps clearly.

The approach works great in ideal cases only. Real data rarely stays ideal forever. I share these points to help you avoid pitfalls. You build better systems with awareness here. But practice reveals more edge cases daily.

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ProfRon
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Explain the limitation of Dijkstra’s algorithm

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