Parallel algorithm for non-monotone DR-submodular maximization
Ene, Alina; Nguyen, Huy Le
In this work, we give a new parallel algorithm
for the problem of maximizing a non-monotone
diminishing returns submodular function subject
to a cardinality constraint. For any desired accuracy𝜖, our algorithm achieves a 1/e − 𝜖 approximation
using O(log n log(1/𝜖 )/𝜖^3) parallel
rounds of function evaluations. The approximation
guarantee nearly matches the best approximation
guarantee known for the problem in the sequential
setting and the number of parallel rounds
is nearly-optimal for any constant 𝜖. Previous algorithms
achieve worse approximation guarantees
using Ω
(log^2 n) parallel rounds. Our experimental
evaluation suggests that our algorithm obtains
solutions whose objective value nearly matches
the value obtained by the state of the art sequential
algorithms, and it outperforms previous parallel
algorithms in number of parallel rounds, iterations,
and solution quality.
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