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Broadcast scheduling in multihop Wireless Sensor Networks (WSNs) is an effective mechanism to perform interference-aware broadcasting. Existing works provide centralized solutions, which cannot be implemented locally. Additionally, they consider very elementary network and interference models, in which, either all sensor nodes have the same transmission range or their transmission ranges are equal to their interference ranges that are not very practical. Furthermore, they entirely ignore the existence of WSNs in 3D. In this paper, we study the broadcast scheduling in 2D and 3D WSNs. We consider that sensor nodes may have different transmission ranges and their interference ranges are α times of their transmission ranges (where α >; 1). We devise efficient coloring methods for coloring a hexagonal tiling in 2D plane and a truncated octahedron tiling in 3D space, based on which we propose O(1)-centralized approximation algorithms and O(1)-localized approximation algorithms for the broadcast scheduling problem in 2D and 3D WSNs, respectively. Our O(1)-centralized approximation algorithms for 3D WSNs and O(1)-localized approximation algorithms for 2D and 3D WSNs are the first approximation algorithms for the corresponding problems. Finally, we present an efficient greedy heuristic to study the effect of various priority metrics for greedily scheduling multiple interfering transmissions. Theoretical analysis and experimental results are provided to evaluate the performance of our algorithms.