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.… Click to show full abstract
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.
               
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