  In recent years, there has been a growing interest in games on graphs within
the research community, fueled by their relevance in applications such as
economics, politics, and epidemiology. This paper aims to comprehensively
detail the design decisions involved in developing a time-efficient algorithm
for solving finite reachability and safety games on graphs. The primary
contribution of this work is the introduction of a novel algorithm that
effectively addresses both reachability and safety games by exploiting their
inherent duality. The performance of the proposed algorithm is rigorously
evaluated against traditional methods using a randomized testing framework. The
paper is organized as follows: first, we provide the reader with a theoretical
overview of reachability and safety games, followed by an in-depth discussion
on the construction of the playing arena. A formal definition of reachability
and safety games and a review of traditional algorithms for their resolution
are then presented. Subsequently, the multiple-perspective algorithm is
introduced along with its optimizations. The paper concludes with an extensive
set of experiments and a comprehensive discussion of their results.
