Right now, every node in a Proof of Work system, solves the POW puzzle independently.
Is there any concept of group proof of work, where everyone in the group needs to solve part of the puzzle.
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I believe any function that was not independent would have progress-- a miner with 3x the hashing speed would be first more often than 3x the time. When applied to POW consensus, progress is very bad for decentralization because it directly increases the income/influence of centralized parties/collaborations.
An example of one of these progress bearing non-independent mining constructions would be instead of finding 1 threshold meeting solution for your block, find 10 nonces that give you 10 threshold meeting solutions.
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Describing PoW as a puzzle is not the best of analogies. It is more accurate to describe as a search (i.e. miners are searching for a Proof of Work which satisfies a condition).
While the PoW search can be parallelized, it is not possible that a particular solution can be pieced together from the parallelized work. A searcher either finds the whole the solution or none of the solution.
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It seems to me what OP is asking about is a group of nodes essentially acting as one node (in the sense of the reward) but divvying up search locations for a nonce to search independently in hopes that one of them will find it before other nodes not in the collusion. Think, a 'tribe' of nodes that then shares earnings. – Prince M Jun 26 '18 at 23:42
