Scalable and Adaptive Algorithms for the Triangle Interdiction Problem on Billion-Scale Networks

Motivated by the relevance of clustering or transitivity to a variety of network applications, we study the Triangle Interdiction Problem (TIP), which is to find a minimum-size set of edges that intersects all triangles of a network. As existing approximation algorithms for this NP-hard problem either do not scale well to massive networks or have poor solution quality, we formulate two algorithms, TARL and DART, with worst-case guarantees 5/2 and 3 with respect to optimal, respectively. Furthermore, DART is able to efficiently maintain its worst-case guarantee under dynamic edge insertion and removal to the network. In our comprehensive experimental evaluation, we demonstrate that DART is able to run on networks with billions of triangles within 2 hours and is able to dynamically update its solution in microseconds.