Section: Overall Objectives
Introduction
The Roma project aims at designing models, algorithms, and scheduling strategies to optimize the execution of scientific applications.
Scientists now have access to tremendous computing power. For instance, the four most powerful computing platforms in the TOP 500 list [68] each includes more than 500,000 cores and deliver a sustained performance of more than 10 Peta FLOPS. The volunteer computing platform BOINC [64] is another example with more than 440,000 enlisted computers and, on average, an aggregate performance of more than 9 Peta FLOPS. Furthermore, it had never been so easy for scientists to have access to parallel computing resources, either through the multitude of local clusters or through distant cloud computing platforms.
Because parallel computing resources are ubiquitous, and because the available computing power is so huge, one could believe that scientists no longer need to worry about finding computing resources, even less to optimize their usage. Nothing is farther from the truth. Institutions and government agencies keep building larger and more powerful computing platforms with a clear goal. These platforms must allow to solve problems in reasonable timescales, which were so far out of reach. They must also allow to solve problems more precisely where the existing solutions are not deemed to be sufficiently accurate. For those platforms to fulfill their purposes, their computing power must therefore be carefully exploited and not be wasted. This often requires an efficient management of all types of platform resources: computation, communication, memory, storage, energy, etc. This is often hard to achieve because of the characteristics of new and emerging platforms. Moreover, because of technological evolutions, new problems arise, and fully tried and tested solutions need to be thoroughly overhauled or simply discarded and replaced. Here are some of the difficulties that have, or will have, to be overcome:

computing platforms are hierarchical: a processor includes several cores, a node includes several processors, and the nodes themselves are gathered into clusters. Algorithms must take this hierarchical structure into account, in order to fully harness the available computing power;

the probability for a platform to suffer from a hardware fault automatically increases with the number of its components. Faulttolerance techniques become unavoidable for largescale platforms;

the ever increasing gap between the computing power of nodes and the bandwidths of memories and networks, in conjunction with the organization of memories in deep hierarchies, requires to take more and more care of the way algorithms use memory;

energy considerations are unavoidable nowadays. Design specifications for new computing platforms always include a maximal energy consumption. The energy bill of a supercomputer may represent a significant share of its cost over its lifespan. These issues must be taken into account at the algorithmdesign level.
We are convinced that dramatic breakthroughs in algorithms and scheduling strategies are required for the scientific computing community to overcome all the challenges posed by new and emerging computing platforms. This is required for applications to be successfully deployed at very large scale, and hence for enabling the scientific computing community to push the frontiers of knowledge as far as possible. The Roma projectteam aims at providing fundamental algorithms, scheduling strategies, protocols, and software packages to fulfill the needs encountered by a wide class of scientific computing applications, including domains as diverse as geophysics, structural mechanics, chemistry, electromagnetism, numerical optimization, or computational fluid dynamics, to quote a few. To fulfill this goal, the Roma projectteam takes a special interest in dense and sparse linear algebra.
The work in the Roma team is organized along three research themes.

Algorithms for probabilistic environments. In this theme, we consider problems where some of the platform characteristics, or some of the application characteristics, are described by probability distributions. This is in particular the case when considering the resilience of applications in failureprone environments: the possibility of faults is modeled by probability distributions.

Platformaware scheduling strategies. In this theme, we focus on the design of scheduling strategies that finely take into account some platform characteristics beyond the most classical ones, namely the computing speed of processors and accelerators, and the communication bandwidth of network links. In the scope of this theme, when designing scheduling strategies, we focus either on the energy consumption or on the memory behavior. All optimization problems under study are multicriteria.

Highperformance computing and linear algebra. We work on algorithms and tools for both sparse and dense linear algebra. In sparse linear algebra, we work on most aspects of direct multifrontal solvers for linear systems. In dense linear algebra, we focus on the adaptation of factorization kernels to emerging and future platforms. In addition, we also work on combinatorial scientific computing, that is, on the design of combinatorial algorithms and tools to solve combinatorial problems, such as those encountered, for instance, in the preprocessing phases of solvers of sparse linear systems.