An Efficient Dynamic Programming Algorithm for Finding Group Steiner Trees in Temporal Graphs

Abstract

The computation of a group Steiner tree (GST) in various types of graph networks, such as social network and transportation network, is a fundamental graph problem in graphs, with important applications. In these graphs, time is a common and necessary dimension, for example, time information in social network can be the time when a user sends a message to another user. Graphs with time information can be called temporal graphs. However, few studies have been conducted on GST in terms of temporal graphs. This study analyzes the computation of GST for temporal graphs, i.e., the computation of temporal GST (TGST), which is shown to be an NP-hard problem. We propose an efficient solution based on a dynamic programming algorithm for our problem. This study adopts new optimization techniques, including graph simplification, state pruning, and $A^{\ast }$ search, are adopted to dramatically reduce the algorithm search space. Moreover, we consider three extensions for our problem, namely the TGST with unspecified tree root, the progressive search of TGST, and the top-N search of TGST. Results of the experimental study performed on real temporal networks verify the efficiency and effectiveness of our algorithms.