A Survey and Comparative Study of Hard and Soft Real-time Dynamic Resource Allocation Strategies for Multi/Many-core Systems

Multi-/many-core systems are envisioned to satisfy the ever-increasing performance requirements of complex applications in various domains such as embedded and high-performance computing. Such systems need to cater to increasingly dynamic workloads, requiring efficient dynamic resource allocation strategies to satisfy hard or soft real-time constraints. This article provides an extensive survey of hard and soft real-time dynamic resource allocation strategies proposed since the mid-1990s and highlights the emerging trends for multi-/many-core systems. The survey covers a taxonomy of the resource allocation strategies and considers their various optimization objectives, which have been used to provide comprehensive comparison. The strategies employ various principles, such as market and biological concepts, to perform the optimizations. The trend followed by the resource allocation strategies, open research challenges, and likely emerging research directions have also been provided

Analysis of the computational complexity of solving random satisfiability problems using branch and bound search algorithms

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical constraints involving N Boolean variables can be satisfied altogether or not. Widely used solving procedures, as the Davis-Putnam-Loveland-Logeman (DPLL) algorithm, perform a systematic search for a solution, through a sequence of trials and errors represented by a search tree. In the present study, we identify, using theory and numerical experiments, easy (size of the search tree scaling polynomially with N) and hard (exponential scaling) regimes as a function of the ratio alpha of constraints per variable. The typical complexity is explicitly calculated in the different regimes, in very good agreement with numerical simulations. Our theoretical approach is based on the analysis of the growth of the branches in the search tree under the operation of DPLL. On each branch, the initial 3-SAT problem is dynamically turned into a more generic 2+p-SAT problem, where p and 1-p are the fractions of constraints involving three and two variables respectively. The growth of each branch is monitored by the dynamical evolution of alpha and p and is represented by a trajectory in the static phase diagram of the random 2+p-SAT problem. Depending on whether or not the trajectories cross the boundary between phases, single branches or full trees are generated by DPLL, resulting in easy or hard resolutions.Comment: 37 RevTeX pages, 15 figures; submitted to Phys.Rev.