Balanced Hop-Constrained Path Enumeration in Signed Directed Graphs

Hop-constrained path enumeration, which aims to output all the paths from two distinct vertices within the given hops, is one of the fundamental tasks in graph analysis. Previous works about this problem mainly focus on unsigned graphs. Nevertheless, with the ever-growing popularity of online social media, signed graphs with positive and negative edges are becoming increasingly ubiquitous and there is a paucity of balanced paths (i.e., paths with an even number of negative edges) enumeration which makes more sense according to balance theory. Motivated by this, in this paper, we propose a new problem, i.e., enumerate balanced paths with hop constraint (BPHC). A baseline method firstly is proposed by extending the DFS method. To further speed up the efficiency, we construct an almost-satisfy table to instantly correct unbalanced state during the search process. Based on the almost-satisfy table, we develop algorithm BMAS by combining the shortest path length in the process of table update and lookup. We conduct experiments on four real world networks to verify the performance of the proposed algorithms.