A simple deterministic algorithm for symmetric submodular maximization subject to a knapsack constraint - Amanatidis, Georgios; Birmpas, Georgios; Markakis, Evangelos (Information processing letters, 2020)
We obtain a polynomial-time deterministic (2ee−1+ϵ)-approximation algorithm for maximizing symmetric submodular functions under a budget constraint. Although there exist randomized algorithms with better expected performance, our algorithm achieves the best known factor achieved by a deterministic algorithm, improving on the previously known factor of 6. Furthermore, it is simple, combining two elegant algorithms for related problems; the local search algorithm of Feige, Mirrokni and Vondrák [1] for unconstrained submodular maximization, and the greedy algorithm of Sviridenko [2] for non-decreasing submodular maximization subject to a knapsack constraint. •We study symmetric submodular maximization subject to a knapsack constraint.•Submodular functions become monotone when restricted to their local maxima.•They are “almost” monotone on their approximate local maxima.•There is a greedy approach that is robust under small deviations from monotonicity.•There is a 2e/(e−1)-approximation algorithm for symmetric submodular objectives.