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==== Integer weights ==== If the edge weights are integers represented in binary, then deterministic algorithms are known that solve the problem in {{math|''O''(''m'' + ''n'')}} integer operations.<ref>{{citation | last1 = Fredman | first1 = M. L. | author1-link = Michael Fredman | last2 = Willard | first2 = D. E. | author2-link = Dan Willard | doi = 10.1016/S0022-0000(05)80064-9 | mr = 1279413 | issue = 3 | journal = [[Journal of Computer and System Sciences]] | pages = 533β551 | title = Trans-dichotomous algorithms for minimum spanning trees and shortest paths | volume = 48 | year = 1994| doi-access = free }}.</ref> Whether the problem can be solved ''deterministically'' for a ''general graph'' in ''linear time'' by a comparison-based algorithm remains an open question.
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