Sina Algorithm: Proposing a Distributed Agent-driven Algorithm For Solving Convex Hull Problem

Natural computing is a multidisciplinary field at the intersection of computer science and nature, focusing on how natural processes can be mimicked, learned from, or harnessed to solve computational problems. This research addresses the convex hull problem—a well-known task in computational geometry that involves determining the minimal convex polygon enclosing a given set of points in a plane—by exploring nature-inspired solutions. We first present an agent-driven simulation that replicates the natural mechanism for solving the convex hull problem. Subsequently, we optimize the simulation computationally to develop a fast algorithm that achieves a worst-case time complexity of\(\:\:O\left(n\text{log}n\right)\), which is optimal for this problem. Finally, we introduce a distributed computing approach to implement the proposed algorithm, achieving an average execution time complexity of \(\:Avg\left(\frac{n\:log\:n}{m}\right)\), where n denotes the problem size and m the number of computational nodes utilized.