Let G = (V, E) be a directed acyclic graph (dag) with n = |V| and m = |E|. We say that a total ordering ≺ on vertices V is a topological ordering if for every edge (u, v) ∈ E, we have u ∈ v. In this paper, we consider the problem of maintaining a topological ordering subject to dynamic changes to the underlying graph. That is, we begin with an empty graph G = (V, o) consisting of n nodes. The adversary adds m edges to the graph G, one edge at a time. Throughout this process, we maintain an online topological ordering of the graph G.
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机译：令G =（V，E）是n = | V |的有向无环图（dag）。和m = | E |。我们说总订购量＆pr;在顶点上，如果对于每个边（u，v）∈E，我们都有u∈v，则V是拓扑顺序。在本文中，我们考虑保持拓扑顺序在基础图上动态变化的问题。也就是说，我们从一个包含n个节点的空图G =（V，o）开始。对手将m个边添加到图形G，一次添加一个边。在整个过程中，我们维护图G的在线拓扑顺序。
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