Adversarial Multi-Agent Path Finding is Intractable

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

“…Given its potential for modeling many real‐world applications, the MBT has attracted considerable research interest, and several exact (de Sousa et al., 2018; Ivanova, 2019), approximation (Kortsarz and Peleg, 1992; Elkin and Kortsarz, 2003), and heuristics (Scheuermann and Wu, 1984; Hoelting et al., 1996; Hasson and Sipper, 2004; Harutyunyan and Wang, 2010; Harutyunyan and Jimborean, 2014; de Sousa et al., 2018) algorithms have been proposed.…”

“…For arbitrary graphs, the exact approaches include a dynamic programming algorithm (Scheuermann and Wu, 1984) and the ILP models presented by de Sousa et al. (2018) and Ivanova (2019). Currently, the ILP model suggested by de Sousa et al.…”

“…The value $$$$\begin{equation} \textit{TLB}(G,{V}_{0})=\left\lceil {\log}_{2}\frac{|V|}{|{V}_{0}|}\right\rceil \end{equation}$$$$defines a lower bound for the MBT (Ivanova, 2019). It is easy to see that a complete graph needs exactly $$\lceil {\log}_{2}\frac{|V|}{|{V}_{0}|}\rceil $$ steps to broadcast.…”

“…(2020). In distributed systems, the MBT has many applications for the Internet of Things (IoT), Wireless Sensor Networks (WSNs) and Industry 4.0 (Shang et al., 2010; Hocaoğlu and Genç, 2019; Ivanova, 2019). Other applications include communication among telephone networks (Ivanova, 2019), surveillance and reconnaissance (Dekker, 2002), robotics (Bucantanschi et al., 2007; Keshavarz et al., 2011), satellite link topology (Chu and Chen, 2018), and Direct Memory Access (DMA) (Lazard, 1992).…”