Problem
Research questions and friction points this paper is trying to address.
post-disaster shelter camps
spatial modeling
facility placement
rainbow domination
Roman domination
A Graph Theoretic Approach to Spatial Modeling of Post Disaster Shelter Camps Using Rainbow and Roman Domination Parameters
🤖 AI Summary
This study addresses the challenge of post-disaster shelter layout planning, which requires balancing multi-type facility coverage with tiered capacity allocation—a task difficult for traditional methods to optimize jointly. This work proposes a graph-theoretic framework based on rainbow k-domination and Roman domination parameters to model simultaneous facility accessibility and service capacity hierarchies. Theoretically, we design a linear-time algorithm for computing minimum rainbow k-dominating sets on trees, establish novel bounds for both parameters in general graphs, characterize the structural properties under which their extremal values coincide, and prove the NP-completeness of the associated recognition problem. Experimentally, large-scale instances validate the scalability of the proposed model. Overall, this research provides a rigorous mathematical foundation and efficient solution strategies for post-disaster facility location.
📝 Abstract
Effective spatial organization of post-disaster shelter camps is essential for ensuring access to basic services while making efficient use of limited space and resources. In this paper, we propose a graph-theoretic framework for shelter-camp facility placement based on rainbow $k$-domination and Roman domination. Rainbow $k$-domination models the simultaneous accessibility of distinct facility types, such as sanitation units, kitchens, water points, and schools, whereas Roman domination is used to represent services with different capacity levels, illustrated through Wi-Fi deployment. We present an $O(nk)$-time algorithm for finding a minimum rainbow $k$-dominating set of a tree with $n$ vertices, which is linear in $n$ for fixed $k$, and computational experiments confirm its scalability on large instances. For general graphs, we establish new lower and upper bounds on the rainbow $k$-domination number. We further investigate its relationship with Roman domination, derive structural properties of graphs attaining the extremal equality between the two parameters, and prove that recognizing such graphs is NP-hard. These results provide a theoretical foundation for domination-based approaches to facility placement in post-disaster shelter planning.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Rainbow k-domination
Roman domination
Graph theory
Facility placement
NP-hard
🔎 Similar Papers
No similar papers found.
