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A classic result asserts that many geometric structures can be constructed optimally by successively inserting their constituent parts in random order. These randomized incremental constructions (RICs) still work with imperfect randomness: the dynamic operations need only be "locally" random. Much attention has been given recently to inputs generated by Markov sources. These are particularly interesting to study in the framework of RICs, because Markov chains provide highly nonlocal randomness,doi:10.1145/1377676.1377701 dblp:conf/compgeom/ChazelleM08 fatcat:iazpl2ctfjbnfhya666bsg56we