Distributed approximate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e583" altimg="si5.svg"><mml:mi>k</mml:mi></mml:math>-core decomposition and min–max edge orientation: Breaking the diameter barrier

We design distributed algorithms to compute approximate solutions for several related graph optimization problems. All our have round complexity being logarithmic in the number of nodes underlying and particular independent diameter. By using a primal–dual approach, we develop 2(1+ϵ)-approximation algorithm computing coreness values graph, as well min–max edge orientation problem, where goal is orient edges so minimize maximum weighted in-degree. provide lower bounds showing that aforementioned are tight both terms approximation guarantee complexity. Additionally, motivated by fact densest subset problem has an inherent dependency on diameter study weaker version does not suffer from same limitation. Finally, conduct experiments large real-world graphs evaluate effectiveness algorithms.