On the Complexity of Mapping Feasibility in Many-Core Architectures

Many-core architectures enable the concurrent execution of multiple application programs. In this context, the well-known problem of feasibly mapping applications, i.e., their tasks and communication, to such architectures has gained importance due to the large number of cores and limited inter-processor communication capacities. This challenge is tackled by so-called Hybrid Application Mapping (HAM) approaches: These combine a design-time analysis to extract sets of mapping constraints that characterize feasible, respectively optimal mappings with the runtime determination of a concrete mapping in dependence of these mapping constraints and the set of currently available resources. A major strength of HAM approaches has been shown as their ability to give real-time and other guarantees for statically characterized application programs even in highly dynamic workload scenarios while avoiding the pessimism of static resource partitionings. However, finding a feasible mapping is an NP-complete problem. This work discusses arising implications for HAM approaches in general and investigates two exact techniques for solving the mapping constraints at runtime in particular: (I) a problem-specific backtracking approach, and (II) an approach that adopts a general-purpose SAT solver. Experimental results show that the overhead of the general-purpose solver and, in particular, processing and solving the required SAT formulation becomes significant, whereas the problem-specific backtracking technique achieves significantly lower execution times.