Sequence submodular maximization meets streaming

In this paper, we study the problem of maximizing a sequence submodular function in the streaming setting, where the utility function is defined on sequences instead of sets of elements. We encode the sequence submodular maximization with a weighted digraph, in which the weight of a vertex reveals the utility value in selecting a single element and the weight of an edge reveals the additional profit with respect to a certain selection sequence. The edges are visited in a streaming fashion and the aim is to sieve a sequence of at most k elements from the stream, such that the utility is maximized. In this work, we present an edge-based threshold procedure, which makes one pass over the stream, attains an approximation ratio of $$(1/(2\varDelta +1)- O(\epsilon ))$$ ( 1 / ( 2 Δ + 1 ) - O ( ϵ ) ) , consumes $$O(k\varDelta /\epsilon )$$ O ( k Δ / ϵ ) memory source in total and $$O(\log (k\varDelta )/\epsilon )$$ O ( log ( k Δ ) / ϵ ) update time per edge, where $$\varDelta $$ Δ is the minimum of the maximal outdegree and indegree of the directed graph.