This paper studies truth maintenance and belief revision tasks on singly-connected structures for the purpose of understanding how structural features could be exploited in such tasks. We present distributed algorithms and show that, in the JTMS framework, both belief revision and consistency maintenance are linear in the size of the knowledge-base on singly-connected structures. However, the ATMS task is exponential in the branching degree of the network. The singly-connected model, while restrictive, is useful for three reasons. First, efficient algorithms on singly-connected models can be utilized in more general structures by employing well-known clustering techniques. Second, these algorithms can serve as approximations or as heuristics in algorithms that perform truth maintenance on general problems. Finally, the analysis provides insights for understanding the sources of the computational difficulties associated with JTMS and ATMS.
Dechter, R., & Dechter, A. (2002). Structure-driven algorithms for truth maintenance. Artificial Intelligence, 82(1–2), 1–20. https://doi.org/10.1016/0004-3702(94)00096-4