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 \((1/(2\varDelta +1)- O(\epsilon ))\), consumes \(O(k\varDelta /\epsilon )\) memory source in total and \(O(\log (k\varDelta )/\epsilon )\) update time per edge, where \(\varDelta \) is the minimum of the maximal outdegree and indegree of the directed graph.

在本文中，我们研究了在流设置中最大化序列次模函数的问题，其中效用函数是在序列上而不是元素集上定义的。我们用加权有向图对序列亚模最大化进行编码，其中顶点的权重揭示了选择单个元素时的效用值，而边缘的权重则揭示了相对于某些选择序列而言的额外收益。以流方式访问边缘，目的是从流中筛选最多k个元素的序列，以使效用最大化。在这项工作中，我们提出了一种基于边缘的阈值过程，该过程在流上进行了一次遍历，获得了\（（1 /（2 \ varDelta +1）-O（\ epsilon））\）的近似比率，\（O（k（var \ varDelta / \ epsilon）\）总共的内存源和\（O（\ log（k \ varDelta）/ \ epsilon）\）每个边的更新时间，其中\（\ varDelta \）为最小有向图的最大出度和入度的关系。