Solving the non-submodular network collapse problems via Decision Transformer

Abstract

Given a graph G, the network collapse problem (NCP) selects a vertex subset S of minimum cardinality from G such that the difference in the values of a given measure function f(G)−f(G∖S) is greater than a predefined collapse threshold. Many graph analytic applications can be formulated as NCPs with different measure functions, which often pose a significant challenge due to their NP-hard nature. As a result, traditional greedy algorithms, which select the vertex with the highest reward at each step, may not effectively find the optimal solution. In addition, existing learning-based algorithms do not have the ability to model the sequence of actions taken during the decision-making process, making it difficult to capture the combinatorial effect of selected vertices on the final solution. This limits the performance of learning-based approaches in non-submodular NCPs.To address these limitations, we propose a unified framework called DT-NC, which adapts the Decision Transformer to the Network Collapse problems. DT-NC takes into account the historical actions taken during the decision-making process and effectively captures the combinatorial effect of selected vertices. The ability of DT-NC to model the dependency among selected vertices allows it to address the difficulties caused by the non-submodular property of measure functions in some NCPs effectively. Through extensive experiments on various NCPs and graphs of different sizes, we demonstrate that DT-NC outperforms the state-of-the-art methods and exhibits excellent transferability and generalizability.