Nguyen Hoang Son

This paper addresses the critical challenge of identifying cost-effective coalitions of social media influencers to promote environmental sustainability (ES) messages under budget constraints. Traditional influencer marketing often relies on heuristics that ignore relational dependencies and heterogeneous agent costs, leading to redundant coverage and suboptimal resource allocation. To overcome these limitations, we introduce a novel Relational Cooperative Game (RG) framework that formalizes pre-determined dependencies among influencers and followers using closure operators, enabling a portfolio of polynomial-time identification algorithms for Minimal Winning Coalitions (MWCs). We further extend this model to the Weighted Cost-Relational Game (WCRG) to optimize campaigns with heterogeneous influencer costs. We prove that finding a Minimum-Cost Winning Coalition (MCWC) is NP-hard via reduction from weighted set cover and propose two complementary algorithms: (1) a Greedy Cost–Benefit (GCB) algorithm that operates in polynomial time and empirically achieves optimal solutions across all tested instances; a logarithmic approximation guarantee is established for the restricted single-antecedent model; and (2) an Integer Linear Programming (ILP) formulation enhanced with Strongly Connected Component (SCC) preprocessing to handle cyclic dependencies and yield exact optimal solutions for moderate instances. Extensive empirical validation, ranging from a representative six-agent cyclic scenario to large-scale synthetic networks (up to 300 agents), confirms the framework’s robustness and scalability. Results demonstrate that GCB consistently achieves optimal solutions (approximation ratio = 1.000×) with subsecond runtime (<0.2 s) and minimal memory overhead (<50 MB), while ILP-SCC leverages graph condensation for rapid exact solving. Compared to size-based baselines, WCRG achieves up to 95.2% cost savings by systematically leveraging cost-efficient micro-influencers, empirically validating that minimizing coalition size does not guarantee cost efficiency. These findings establish WCRG as a scalable, budget-aware optimization toolkit for maximizing the impact of sustainability campaigns through relational coalition design.

The integration of aquaculture and agriculture (IAA) of the home lot, garden, livestock and fishpond, and rice field is referred to as the VACR system (a Vietnamese acronym: Vuon = garden, Ao = pond, Chuong = livestock pen, Ruong = rice field), not only reduce poverty, increase productivity, diversified income streams, enhanced food security but also promote biodiversity, and sustainable agricultural practices. In the perspectives of sharing economy, within a farmer’s home lot, the garden encompasses the production of various plants bearing fruits and vegetables; the shed includes livestock production; the fishpond provides aquaculture production, mainly fish and shrimp; and finally, the rice field is mainly the production of rice, a staple main food for many cultures. All elements of this production system provide food security for human. In addition, in the perspectives of circular economy, the four elements are also complementary one another, where the fishpond acts as a source of water and mud for the garden and rice-field, thereby nourishing it; the garden and rice-field provides feed for fish and livestock; and the animal stool complementarily used as fish/shrimp feed or fertilizer for the garden and rice field; also, rice field yield rice straw for livestock bedding. That VACR system, applied into a low-income famer family, could be expanded into an integrated multiple low-to-middle-income-farmer-family coalition of non-pesticide vegetable farmer family, rice farming family, shrimp farmer family, and animal raising family for the sake of both resource sharing and waste management to make the agriculture supply chain ecosystem more sustainable and efficiency. This study investigates the evolutionary game dynamics among four-party cooperation under supports/non-supports by government in the context of resource sharing and waste management aiming to increase efficiency, reduce waste, and maximize the utilization of public resources. To understand the behavior of different stakeholders under government incentive policies, we develop a multifaceted five-way evolutionary game model involving a local government (G) and a VACR synergy of four farmer families of a non-pesticide rice farming family (A), a non-pesticide vegetable farmer family (B), a plant-feed animal raising (C), and a shrimp farmer family (D). Through stability analysis, we explore equilibrium conditions of evolutionarily stable strategies (ESSs) for the quintuple evolutionary game. To ensure the robustness of our findings, we conduct a MATLAB simulation analysis, based on VACR synergy applied in Vietnam’s Mekong delta data to validate the analytical results. Our findings highlight that government supports and subsidies, the costs incurred by all parties in VACR synergy to share resource and manage waste to increase productivity, reduce reliance on external inputs, promoting sustainable and resilient farming systems, and the additional distribution income/profits derived from this synergy are critical in determining whether the evolutionary game can achieve a stable equilibrium state. This research enables all parties in VACR synergy to optimize the use of shared resources, waste management, lower operating costs, and enhance efficiency and sustainability. Additionally, government subsidy policies play a crucial role in encouraging all parties in synergy to engage in resource sharing, thereby fostering more efficiency, resource optimization, innovation, waste reduction, and collaboration to better serve agricultural supply chain ecosystem. Based on these insights, the paper offers practical recommendations to further promote the resource sharing and circular economy in agricultural production practices.

In this paper, we study how to approach some combinatorial problems of closure operations using a hypergraph. We prove that all minimal keys of the closure operations can be represented with the transversal hypergraph of a family. We establish the relationship between anti keys and minimal keys of the closure operations in the hypergraph. Trong bài báo này chúng tôi nghiên cứu cách tiếp cận một số vấn đề về tổ hợp của toán tử bao đóng bằng mô hình siêu đồ thị. Chúng tôi đưa ra biểu diễn tất cả khóa tối thiểu của toán tử bao đóng qua siêu đồ thị transversal. Sử dụng siêu đồ thị, chúng tôi thiết lập mối quan hệ giữa phản khóa và khóa tối thiểu của toán tử bao đóng.

As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense families, including the collection of the whole closed sets and the minimal generator of the closed sets, are also pointed out. More important, a necessary and sufficient condition for an arbitrary family to be dense is provided in our paper. Then we use these dense families to characterize minimal keys of the closure operation under the viewpoint of transversal hypergraphs and construct an algorithm for determining the minimal keys of a closure operation.

In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and antikeys of closure operations based on independent sets. We construct two combinatorial algorithms for finding all minimal keys and all antikeys of a given closure operation based on independent sets. We estimate the time complexity of these algorithms. Finally, we give an NP-complete problem concerning nonkeys of closure operations.

Scheduling is one of the activities which have a great impact on the communication performance of optical burst switching networks. There have been many scheduling algorithms proposed but most of them are online. Recently, several algorithms of group scheduling have been published, but they have the complexity of NP-complete. Moreover, the timeslot of group scheduling is predetermined and fixed without considering the dependence on the rate of arriving data. This article proposes a new algorithm of group scheduling which has the linear complexity and has the timeslot of group scheduling that could be changeable and adapt to the rate of arriving data. The analyses and evaluations of the effectiveness based on the simulation results will confirm the advantages of our algorithm.