Achlioptas process: minimize product rule vs Erdős-Rényi
Edges added: — | Giant component: —
Explosive percolation (Achlioptas 2009): at each step, pick k random candidate edges; add the one minimizing the product of the two cluster sizes it would connect. This suppresses giant component formation, then causes an apparently discontinuous "explosion" near the threshold. Compare to Erdős-Rényi (random edge addition, continuous transition at p=1/2N). Both shown: blue = Explosive, orange = ER. The sharp jump in blue is the signature "explosive" transition.