Sublinear-time identification of the maximum greedy marginal gain

Determine whether the vertex maximizing the current Independent Cascade influence marginal gain can be identified in sublinear time relative to the exact all-marginals computation, specifically in o(nf(w)) time, without materializing the complete gradient.

Background

The proposed algorithm computes every candidate marginal gain by reverse-mode differentiation through an exact bounded-treewidth inference circuit, requiring O(nf(w)) time per greedy iteration, where f(w)=2^{O(w^2)}poly(w). Classical greedy selection, however, requires only the largest marginal gain rather than the complete gradient.

The paper therefore raises the unresolved possibility of exploiting the structure of the inference computation, lazy-greedy upper bounds, or the fact that successive seed sets differ by one vertex to identify the maximizing candidate faster than explicitly computing all marginal gains.