TDB: Breaking All Hop-Constrained Cycles in Billion-Scale Directed Graphs

TL;DR

This paper introduces TDB, a top-down approach for breaking all hop-constrained cycles in billion-scale directed graphs, improving efficiency over traditional bottom-up methods.

Contribution

It proposes a novel top-down algorithm for the hop-constrained cycle cover problem, with theoretical bounds and enhanced practical performance.

Findings

The top-down method outperforms bottom-up approaches in large-scale graphs.

Theoretical bounds demonstrate improved complexity.

Experimental results show faster cycle coverage in billion-scale graphs.

Abstract

The Feedback vertex set with the minimum size is one of Karp's 21 NP-complete problems targeted at breaking all the cycles in a graph. This problem is applicable to a broad variety of domains, including E-commerce networks, database systems, and program analysis. In reality, users are frequently most concerned with the hop-constrained cycles (i.e., cycles with a limited number of hops). For instance, in the E-commerce networks, the fraud detection team would discard cycles with a high number of hops since they are less relevant and grow exponentially in size. Thus, it is quite reasonable to investigate the feedback vertex set problem in the context of hop-constrained cycles, namely hop-constrained cycle cover problem. It is concerned with determining a set of vertices that covers all hop-constrained cycles in a given directed graph. A common method to solve this is to use a bottom-up algorithm, where it iteratively selects cover vertices into the result set. Based on this paradigm, the existing works mainly focus on the vertices orders and several heuristic strategies. In this paper, a totally opposite cover process topdown is proposed and bounds are presented on it. Surprisingly, both theoretical time complexity and practical performance are improved.