International audienceThis paper elaborates on a new view on software pipelining, called decomposed software pipelining. The approach is to decouple the problem into resource constraints and dependence constraints. Resource constraints management amounts to scheduling an acyclic graph subject to resource constraints for which an efficiency bound is known, resulting in a bound for loop scheduling. The acyclic graph is obtained by cutting some particular edges of the (cyclic) dependence graph. In this paper, we cut edges in a different way, using circuit retiming algorithms, so as to minimize both the longest dependence path in the acyclic graph, and the number of edges in the acyclic graph. With this technique, we improve the efficiency bound given for Gasperoni and Schwlegelshohn algorithm, and we reduce the constraints that remain for the acyclic problem. We believe this framework to be of interest because it brings a new insight into the software problem by establishing its deep link with the circuit retiming proble

In the framework of perfect loop nests with uniform dependences, tiling has been extensively studied as a source-to-source program transformation. Little work has been devoted to the mapping and scheduling of the tiles on to physical processors. We present several new results in the context of limited computational resources, and assuming communication-computation overlap. In particular, under some reasonable assumptions, we derive the optimal mapping and scheduling of tiles to physical processors.

The determination of the configuration of a protein in three-dimensional (3D) space constitutes one of the major challenges in molecular biology research today. A method consists in choosing a protein structure from a database that minimizes an energy function. First, we model the problem in terms of dynamic programming and show that the determination of the order in which the variables must be considered to minimize the time complexity is an NP-hard problem. Second, we propose a new decomposition algorithm of the threading problem that is based on the connectivity of the graph induced by the 3D structure of a protein. Our decomposition could be used to solve the threading problem. The goal in this paper is to evaluate the intrinsic complexity of 3D structure, which can be viewed as information that may be incorporated into a solution method. It provides two indexes of complexity (time and space) and determines in polynomial time complex components of the 3D structure of a protein.

In the framework of fully permutable loops, tiling is a compiler technique (also known as 'loop blocking') that has been extensively studied as a source-to-source program transformation. Little work has been devoted to the mapping and scheduling of the tiles on to physical parallel processors. We present several new results in the context of limited computational resources and assuming communication-computation overlap. In particular, under some reasonable assumptions, we derive the optimal mapping and scheduling of tiles to physical processors.