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We introduce a guided network growth model, which we call the degree productrule process, that uses solely local information when adding new edges. Forsmall numbers of candidate edges our process gives rise to a second order phasetransition, but becomes first order in the limit of global choice. We providethe set of critical exponents required to characterize the nature of thispercolation transition. Such a process permits interventions which can delaythe onset of percolation while tempering the explosiveness caused by clusterproduct rule processes.

Degree product rule tempers explosive percolation in the absence of global information