Abstract

We address the logical topology design problem (LTD) in WDM transport networks under static traffic assumptions. We start with one of the standard MILP formulations of the LTD problem that aims at optimizing the network congestion. We propose an improvement to this model that additionally optimizes the average hop count. We then derive a new MILP model that compels the traffic to be atomically routed. This last model enables fair comparisons of solutions obtained with MILP formulations and with metaheuristic algorithms. The latter allow us to deal with large size networks whereas the former are limited by their computational complexity. In this paper Tabu Search is used to tackle the LTD problem. We compare and discuss the logical topologies computed by the various methods described in the paper. Document type: Part of book or chapter of book

Abstract

International audience; Mapping applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline or fork graphs. Several antagonist criteria should be optimized for workflow applications, such as throughput and latency (or a combination). In this paper, we consider a simplified model with no communication cost, and we provide an exhaustive list of complexity results for different problem instances. Pipeline or fork stages can be replicated in order to increase the throughput by sending consecutive data sets onto different processors. In some cases, stages can also be data-parallelized, i.e. the computation of one single data set is shared between several processors. This leads to a decrease of the latency and an increase of the throughput. Some instances of this simple model are shown to be NP-hard, thereby exposing the inherent complexity of the mapping problem. We provide polynomial algorithms for other problem instances. Altogether, we provide solid theoretical foundations for the study of mono-criterion or bi-criteria mapping optimization problems. Document type: Report

Abstract

Mapping workflow applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline graphs. Several antagonist criteria should be optimized, such as throughput and latency (or a combination). In this paper, we study the complexity of the bi-criteria mapping problem for pipeline graphs on communication homogeneous platforms. In particular, we assess the complexity of the well-known chains-to-chains problem for different-speed processors, which turns out to be NP-hard. We provide several efficient polynomial bi-criteria heuristics, and their relative performance is evaluated through extensive simulations.; L’ordonnancement et l’allocation des workflows sur plates-formes parallèles est un problème crucial, même pour des applications simples comme des graphes en pipeline. Plusieurs critères contradictoires doivent être optimisés, tels que le débit et la latence (ou une combinaison des deux). Dans ce rapport, nous étudions la complexité du problème de l’ordonnancement bi-critère pour les graphes pipelinés sur des plate-formes avec communications homogènes. En particulier nous évaluons la complexité du problème bien connu ”chains-on-chains” pour les processeurs hétérogènes, un problème qui s’avère NP-difficile. Nous proposons plusieurs heuristiques bi-critères efficaces en temps polynomial. Leur performance relative est évaluée par des simulations intensives. Document type: Report