There are many answered questions on Internet related to the calculation of space complexity of different algorithms. All the algorithms are centralized in nature. How can we calculate the space complexity of semi-centralized and distributed algorithms? The distributed algorithms run on multiple servers. Should the space complexity of each server be calculated separately?
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The number of servers is finite so should not impact the complexity calculation ideally for Asymptotic notation. If you still want to show what memory consumption approaches to as number of servers reach a high value, you will need to multiple memory complexity on each server with the number of servers.