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Is Graph Isomorphism solvable in Polynomial Time?
In graph theory, two graphs are isomorphic if there is a one-to-one correspondence between their vertex sets (details here). The computational task of determining whether two graphs are isomorphic is known as the graph isomorphism problem. The problem arises in many applications, for example, in electronic design automation when one needs a demonstration that two circuit representations are equivalent.
The question of whether graph isomorphism is always solvable in polynomial time is a major open problem in computer science. The problem belongs to NP, but it has not yet been determined whether it is P or NP-complete.
A new breakthrough in the graph isomorphism problem is implied by the abstract of a theoretical computer science seminar scheduled for Nov. 10th, 2015 at the University of Chicago.
By June 1, 2017, will the graph isomorphism problem have been proved to always be solvable in polynomial time?
Metaculus help: Predicting
Predictions are the heart of Metaculus. Predicting is how you contribute to the wisdom of the crowd, and how you earn points and build up your personal Metaculus track record.
The basics of predicting are very simple: move the slider to best match the likelihood of the outcome, and click predict. You can predict as often as you want, and you're encouraged to change your mind when new information becomes available. With tachyons you'll even be able to go back in time and backdate your prediction to maximize your points.
The displayed score is split into current points and total points. Current points show how much your prediction is worth now, whereas total points show the combined worth of all of your predictions over the lifetime of the question. The scoring details are available on the FAQ.
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Metaculus help: Community Stats
Use the community stats to get a better sense of the community consensus (or lack thereof) for this question. Sometimes people have wildly different ideas about the likely outcomes, and sometimes people are in close agreement. There are even times when the community seems very certain of uncertainty, like when everyone agrees that event is only 50% likely to happen.
When you make a prediction, check the community stats to see where you land. If your prediction is an outlier, might there be something you're overlooking that others have seen? Or do you have special insight that others are lacking? Either way, it might be a good idea to join the discussion in the comments.