Abstract—
In this paper, we introduce the notion of sufficient set and necessary set for distributed processing of probabilistic top-k queries in cluster-based wireless sensor networks. These two concepts have very nice properties that can facilitate localized data pruning in clusters. Accordingly, we develop a suite of algorithms, namely, sufficient set-based (SSB), necessary set-based (NSB), and boundary-based (BB), for intercluster query processing with bounded rounds of communications. Moreover, in responding to dynamic changes of data distribution in the network, we develop an adaptive algorithm that dynamically switches among the three proposed algorithms to minimize the transmission cost. We show the applicability of sufficient set and necessary set to wireless sensor networks with both two-tier hierarchical and tree-structured network topologies. Experimental results show that the proposed algorithms reduce
data transmissions significantly and incur only small constant rounds of data communications. The experimental results also demonstrate the superiority of the adaptive algorithm, which achieves a near-optimal performance under various conditions.

Existing System with Limitations

In cluster-based wireless sensor networks, the processing of probabilistic top-k queries poses several challenges. Current systems face the following limitations:

1. High Data Transmission Costs: Existing systems often involve significant data transmission between clusters, leading to high energy consumption and reduced network lifetime.
2. Inefficient Query Processing: Traditional methods for processing top-k queries do not effectively leverage localized data pruning, resulting in inefficient query processing.
3. Static Algorithms: Many existing approaches use static algorithms that do not adapt to dynamic changes in data distribution within the network, leading to suboptimal performance under varying conditions.
4. Excessive Communication Rounds: Current systems may require numerous communication rounds to process queries, increasing latency and further consuming network resources.
5. Limited Applicability: Existing methods may not be well-suited for different network topologies, such as two-tier hierarchical or tree-structured networks, limiting their versatility.

Proposed System with Advantages

The proposed system introduces the concepts of sufficient set and necessary set for distributed processing of probabilistic top-k queries in cluster-based wireless sensor networks, addressing the limitations of existing systems:

1. Localized Data Pruning: By leveraging the properties of sufficient and necessary sets, the system enables efficient localized data pruning within clusters, reducing the amount of data that needs to be transmitted.
2. Suite of Efficient Algorithms: The proposed system includes three algorithms—sufficient set-based (SSB), necessary set-based (NSB), and boundary-based (BB)—that facilitate intercluster query processing with bounded rounds of communications.
3. Adaptive Algorithm: An adaptive algorithm dynamically switches among the three proposed algorithms based on the current data distribution, minimizing transmission costs and improving overall efficiency.
4. Reduced Data Transmissions: Experimental results show that the proposed algorithms significantly reduce data transmissions, enhancing the energy efficiency and extending the network lifetime.
5. Constant Rounds of Communication: The system incurs only a small, constant number of communication rounds, reducing latency and conserving network resources.
6. Versatile Network Topology Support: The applicability of sufficient and necessary sets is demonstrated for both two-tier hierarchical and tree-structured network topologies, making the system versatile and adaptable to different network configurations.
7. Near-Optimal Performance: The adaptive algorithm achieves near-optimal performance under various conditions, as evidenced by experimental results, ensuring robust and reliable query processing across different scenarios.

By addressing the limitations of existing systems, the proposed approach enhances the efficiency and effectiveness of probabilistic top-k query processing in cluster-based wireless sensor networks.