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Structure learning is essential for Bayesian networks (BNs) as it uncovers causal relationships, and enables knowledge discovery, predictions, inferences, and decision-making under uncertainty. Two novel algorithms, FSBN and SSBN, based on the PC algorithm, employ local search strategy and conditional independence tests to learn the causal network structure from data. They incorporate d-separation to infer additional topology information, prioritize conditioning sets, and terminate the search immediately and efficiently. FSBN achieves up to 52% computation cost reduction, while SSBN surpasses it with a remarkable 72% reduction for a 200-node network. SSBN demonstrates further efficiency gains due to its intelligent strategy. Experimental studies show that both algorithms match the induction quality of the PC algorithm while significantly reducing computation costs. This enables them to offer interpretability …