Polynomial-time representative selection on general graphs

Develop a representative-selection mechanism for general delegation graphs that preserves the properties of the proposed proportional-representation mechanism while remaining computable in polynomial time.

Background

The paper introduces a representative-selection mechanism based on Random Walk Decay and proves that the resulting optimization problem is polynomial-time computable for functional graphs. For general graphs, however, the corresponding optimization problem is shown to be NP-hard.

The conclusion therefore identifies the need for a different or generalized representative-selection mechanism that retains the desirable properties established for the proposed method while achieving polynomial-time computation on general graphs.