The influence maximization problem has gained particular importance in viral marketing for large-scale spreading in social networks. Developing a fast and appropriate algorithm to identify an optimized seed set for the diffusion process on social networks is crucial due to the fast growth of networks. Most fast methods only focus on the degree of nodes while ignoring the strategic position of nodes in the networks. These methods do not have the required quality in finding a seed set in most networks. On the other hand, many other methods have acceptable quality, but their computational overhead is significant. To address these issues, the main concentration of this paper is to propose a fast and accurate method for the influence maximization problem, which uses a local traveling for labeling of nodes based on the influence power, called the LMP algorithm. In the proposed LMP algorithm, first, a travel starts from a node with the lowest influence power to assign a ranking-label for this node and its neighbor nodes in each step based on their diffusion capability and strategic position. The LMP algorithm uses node labeling steps to reduce search space significantly. Three ranking-labels are used in the proposed algorithm, and nodes with the highest ranking-label are selected as candidate nodes. This local and fast step strictly reduces the search space. Finally, the LMP algorithm selects seed nodes based on the topology features and the strategic position of the candidate and connector. The performance of the proposed algorithm is benchmarked with the well-known and recently proposed seed selection algorithms. The experimental results are performed on real-world and synthetic networks to validate the efficiency and effectiveness. The experiments exhibit that the proposed algorithm is the fastest in comparison with other state-of-the-art algorithms, and it has linear time complexity. In addition, it can achieve a good tradeoff between the efficiency and time complexity in the influence maximization problem. •To propose a fast and accurate method for the influence maximization problem.•A local traveling is used to select candidate nodes for node labeling based on their diffusion capability.•The LMP algorithm uses node labeling step to reduce significantly search space.•Seed nodes are selected from the candidate and specially connector nodes based on the topology features and the specific position.•The proposed algorithm has the best stability, accuracy and running time than other well-known and fast algorithms.•The proposed algorithm does not use any adjustable parameters in steps of algorithms.