Abstract
This paper introduces a polynomially focused methodology for addressing the subset sum problem and evaluates its relevance to unstructured information retrieval. The research addresses the challenge of determining a subset of positive integers that totals a certain target value and formulates an accurate solution framework utilizing combinatorial mappings, symmetry characteristics of binomial coefficients, and a merge-based building method. The core concept of the proposed methodology is to condense the original combinatorial parameter into a more compact search structure, thereby reducing the number of potential combinations and enhancing computational feasibility. Based on this, generalized methodologies for the subset sum issue and associated k-SUM formulations are established. The results indicate that the suggested method can streamline the exact search process relative to traditional exponential or pseudo-polynomial approaches, while maintaining solution accuracy. The practical relevance of the approach pertains to search activities inside extensive and unstructured data environments, where effective filtering and combination matching are crucial. In the context of sustainable development, the proposed method contributes to the design of more resource-efficient digital intelligence systems by reducing redundant search operations, memory usage, and computational overhead in large-scale information processing tasks. Such efficiency is important for sustainable decision-support systems, including public administration, environmental monitoring, smart-city services, and policy-oriented information retrieval.