更新时三角形的维护
Maintaining Triangle Queries under Updates
摘要：
我们考虑的问题，增量维护三角形查询与任意自由变量下的单元组更新的输入关系。我们介绍了一种称为IVM $^ε$的方法，表现出更新时间，空间和查询结果的枚举延迟之间的权衡，使得更新时间的范围从平方根到线性的数据库大小，而延迟的范围从常数到线性时间。IVM $^ε$在基于在线矩阵向量乘法猜想的更新延迟空间中实现了Pareto最坏情况最优。该算法对于自由变量为零或三的三角查询是强Pareto最优的，对于自由变量为一或两的三角查询是弱Pareto最优的。
英文摘要：
We consider the problem of incrementally maintaining the triangle queries with arbitrary free variables under single-tuple updates to the input relations. We introduce an approach called IVM$^ε$ that exhibits a trade-off between the update time, the space, and the delay for the enumeration of the query result, such that the update time ranges from the square root to linear in the database size while the delay ranges from constant to linear time. IVM$^ε$ achieves Pareto worst-case optimality in the update-delay space conditioned on the Online Matrix-Vector Multiplication conjecture. It is strongly Pareto optimal for the triangle queries with zero or three free variables and weakly Pareto optimal for the triangle queries with one or two free variables.
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