Inapproximability and polynomial-time approximation algorithm for UET tasks on structured processor networks (Q666411)

Summary: We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter \(\delta \in \mathbb N\). We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time \(O(\delta^2)\)-approximation algorithm for the makespan minimization on processor networks with diameter \(\delta\).