We consider the consensus interdiction problem (CIP), in which the goal is to maximize the convergence time of consensus dynamics subject to removing a limited number of network edges. We first show that CIP can be cast as an effective resistance interdiction problem (ERIP), in which the goal is to remove a limited number of network edges to maximize the effective resistance between a source node and a sink node. We show that ERIP is strongly NP-hard, even for bipartite graphs of diameter three with fixed edges incident to the source/sink. We establish the same hardness result for the CIP, hence correcting some claims in the past literature. We then show that both ERIP and CIP do not admit polynomial-time approximation schemes, and moreover, they cannot be approximated up to a (nearly) polynomial factor assuming exponential time hypothesis. Subsequently, we devise a polynomial-time $mn$-approximation algorithm for the ERIP that only depends on the number of nodes $n$ and the number of edges $m$, but is independent of the size of edge resistances. Finally, using a quadratic program formulation for the CIP, we devise an approximation algorithm to find a local optimal solution for the CIP.

翻译：我们考虑的是共识阻截问题(CIP ), 目标是最大限度地缩短共识动态的趋同时间,但须消除有限的网络边缘。 我们首先表明,CIP 可以被描绘成一个有效的阻截问题(ERIP ), 目标是消除数量有限的网络边缘, 以最大限度地扩大源节点和汇节点之间的有效抵抗力。 我们显示, ERIP 强烈的NP- 硬性, 即使是直径3的双面图, 直径3号, 与源/ 汇有固定边缘事件 。 我们为 CIP 设定相同的硬性结果, 从而纠正过去文献中的一些主张。 然后我们表明, ERIP 和 CIP 都不接受多时近计划, 此外, 其近似于( 近于) 多元性因素, 假设指数性时间 。 随后, 我们为ERIP 设计了一个多边- 时间 $mmun- adoprognomation 算法, 仅取决于点数和边缘数 $m$, 但纠正了过去文献中的一些主张。 然后, 我们想方略度方案 。