## 4 D2D Group Communication Scheme with Bidirectional and InCrentental A-Star (BICA*) Routing
### Path Selection Algorithm
A refined BICA* algorithm incorporating the concepts of bidirectional search and lifelong planning is developed for path selection. The proposed path selection algorithm can effectively reduce the search time and quickly react to topological change. Compared with Greedy, TSRS, and standard A*, the proposed scheme surpasses in all aspects, including delay and throughput, with an acceptable computational cost. The performance improvement of the proposed scheme is attributed to the design of the BICA*. The D2D routing problem is regarded as a problem of finding the least-cost path from the source UE to the destination UE. The cost is defined according to the design objectives, namely the least delay and the maximal throughput. The incorporation of bidirectional search and lifelong planning endows the proposed scheme with less computational time and timely reaction in response to topological change. For static environments, BICA* and A* have similar performance in throughput and delay. Both possess performance improvements over TSRS and Greedy, up to 23% and 46.5%, respectively. BICA* outperforms A* in cases of dynamic environments. The advantage of BICA* over A* becomes eminent as the moving speed of UEs increases due to its bidirectional and lifetime-planning natures. As the speed of UEs increased, the average and the satisfaction ratio decreased accordingly for all approaches. However, the proposed BICA* maintains the best performance, disregarding the moving speed. Conceptualization, W.K.L. and C.-P.Y. ; methodology, W.K.L. ; software, C.-P.Y. ; validation, C.-S.S.; formal analysis, C.-P.Y. ; investigation, W.K.L. ; resources, C.-S.S.; writing--original

Figure 11:6 Satisfaction rate vs. group’s moving speed. draft preparation, C.-S.S.; writing--review and editing, W.K.L. ; project administration, W.K.L. ; funding acquisition, C.-S.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. This research was partly supported by the Ministry of Science and Technology, Taiwan under the grant numbers MOST 111-2221-E-110-025 and MOST 111-2221-E-992-066. The authors declare no conflict of interest. ## References

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