6 research outputs found
Nearly Linear-Time, Parallelizable Algorithms for Non-Monotone Submodular Maximization
We study parallelizable algorithms for maximization of a submodular function,
not necessarily monotone, with respect to a cardinality constraint . We
improve the best approximation factor achieved by an algorithm that has optimal
adaptivity and query complexity, up to logarithmic factors in the size of
the ground set, from to . We provide two
algorithms; the first has approximation ratio , adaptivity , and query complexity , while the second has
approximation ratio , adaptivity , and query
complexity . Heuristic versions of our algorithms are empirically
validated to use a low number of adaptive rounds and total queries while
obtaining solutions with high objective value in comparison with highly
adaptive approximation algorithms.Comment: 24 pages, 2 figure