In this paper,we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular(DR-submodular)function and a nonnegative linear function on the integer *** it is almost un...
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In this paper,we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular(DR-submodular)function and a nonnegative linear function on the integer *** it is almost unapproximable for maximizing a submodular function without the condition of nonnegative,we provide weak(bifactor)approximation algorithms for this problem in two online settings,*** the unconstrained online model,we combine the ideas of single-thresholdgreedy,binary search and function scaling to give an efficient algorithm with a 1/2 weak approximation *** the online streaming model subject to a cardinality constraint,we provide a one-pass(3-√5)/2 weak approximation ratio streaming *** memory complexity is(k log k/ε),and the update time for per element is(log^(2)k/ε).
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