Strategic Security Zoning Via Chromatic Graph Theory: An Optimized Patrol Allocation for Nigeria’s Geopolitical Regions.

Abstract:

Geographically distributed security risks throughout Nigeria tend to spread from one state to another via shared borders and movement routes, ensuring the requirement for an optimized and conflict-free security deployment strategy. In this work, a framework for allocating and deploying available security resources in a manner that avoids inter-unit conflicts in a Nigerian setting is proposed by formulating a graph-coloring model that represents the six geopolitical zones in a two-dimensional coordinate plane as map graphs and allocating states as vertices and borders between them as edges. For each zone, a backtracking algorithm based on an adjacency matrix approach is applied with a view to determining the chromatic numbers χ(G) that represent the optimal minimum needed non-conflicting security patrol units and schedules needed to avoid interference and overlap on inter-state levels for enhanced operational efficiency and effectiveness. From the results, it can be observed that while the North-East geopolitical zone has the highest connectivity and insurgent activities, security deployment needs χ(G) = 4 units, whereas for North-Central, North-West, South-East, South-South, and South-West zones, security deployment needs χ(G) = 3 units. This indicates the immediate applicability of security resource allocation into partitioned time schedules for nationwide security patrol network deployment and regional security force coordination. By appropriating map graphs on a plane into a real-time applicability tool, the research highlights the applicability of computational graph theory concepts for optimizing security resource planning from conventional-based approaches toward efficient strategies involving minimum resource spending with the highest operational ranges to achieve the UN Sustainable Development Goal.