The information flows among the people while they communicate through social media websites. Due to the dependency on digital media, a person shares important information or regular updates with friends and family. The set of persons on social media forms a social network. Influence Maximization (IM) is a known problem in social networks. In social networks, information flows from one person to another using an underlying diffusion model. There are two fundamental diffusion models: the Independent Cascade Model (ICM) and the Linear Threshold Model (LTM). In this paper, we study a variant of the IM problem called Minimum Influential Seeds (MINFS) problem proposed by Qiang et al.[16]. It generalizes the classical IM problem with LTM as the diffusion model. Compared to IM, this variant has additional parameters: the influence threshold for each node and the propagation range. The propagation range is a positive integer that specifies how far the information can propagate from a node. A node on the network is not immediately influenced until it receives the same information from enough number of neighbors (influence threshold). Similarly, any node does not forward information until it receives the same information from a sufficient number of neighbors (activation threshold). Once a node becomes activated, it tries to activate or influence its neighbors. The MINFS problem aims to select the minimum number of initial spreader nodes such that all nodes of the graph are influenced. In this paper, we extend the study of the MINFS problem. We propose heuristics that construct seed sets based on the average degree of non-activated nodes, closest first, and backbone-based heaviest path.