A simple deterministic algorithm for symmetric submodular maximization subject to a knapsack constraint

We obtain a polynomial-time deterministic (2e/e-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.