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Abstract-In this paper, we discuss and compare several policies to place replicas in tree networks, subject to server capacity and Quality-of-Service (QoS) constraints. The client requests are known beforehand, while the number and location of the servers are to be determined. The standard approach in the literature is to enforce that all requests of a client be served by the closest server in the tree. We introduce and study two new policies. In the first policy, all requests from a given client are still processed by the same server, but this server can be located anywhere in the path from the client to the root. In the second policy, the requests of a given client can be processed by multiple servers. One major contribution of this paper is to assess the impact of these new policies on the total replication cost. Another important goal is to assess the impact of server heterogeneity, both from a theoretical and a practical perspective. In this paper, we establish several new complexity results and provide several efficient polynomial heuristics for NP-complete instances of the problem. These heuristics are compared one to the other, and their absolute performance is assessed by comparison with the optimal solution provided by an integer linear program. [ABSTRACT FROM AUTHOR]

Abstract: Mapping applications onto parallel platforms is a challenging problem, that becomes even more difficult when platforms are heterogeneous — nowadays a standard assumption. A high-level approach to parallel programming not only eases the application developer’s task, but it also provides additional information which can help realize an efficient mapping of the application. In this paper, we discuss the mapping of pipeline skeletons onto different types of platforms: Fully Homogeneous platforms with identical processors and interconnection links; Communication Homogeneous platforms, with identical links but different-speed processors; and finally, Fully Heterogeneous platforms. We assume that a pipeline stage must be mapped on a single processor, and we establish new theoretical complexity results for different mapping policies: a mapping can be required to be one-to-one (a processor is assigned at most one stage), or interval-based (a processor is assigned an interval of consecutive stages), or fully general. In particular, we show that determining the optimal interval-based mapping is NP-hard for Communication Homogeneous platforms, and this result assesses the complexity of the well-known chains-to-chains problem for different-speed processors. We provide several efficient polynomial heuristics for the most important policy/platform combination, namely interval-based mappings on Communication Homogeneous platforms. These heuristics are compared to the optimal result provided by the formulation of the problem in terms of the solution of an integer linear program, for small problem instances. [Copyright &y& Elsevier]

Abstract: In this paper, we assess the impact of heterogeneity on scheduling independent tasks on master-slave platforms. We assume a realistic one-port model where the master can communicate with a single slave at any time. We target both on-line and off-line scheduling problems, and we focus on simpler instances where all tasks have the same size. While such on-line problems can be solved in polynomial time on homogeneous platforms, we show that there does not exist any optimal deterministic algorithm for heterogeneous platforms. Whether the source of heterogeneity comes from computation speeds, or from communication bandwidths, or from both, we establish lower bounds on the competitive ratio of any deterministic algorithm. We provide such bounds for the most important objective functions: the minimization of the makespan (or total execution time), the minimization of the maximum response time (difference between completion time and release time), and the minimization of the sum of all response times. Altogether, we obtain nine theorems which nicely assess the impact of heterogeneity on on-line scheduling. For off-line scheduling, we prove several result for problems with release dates, either optimality or NP-hardness. These theoretical contributions are complemented on the practical side by the implementation of several heuristics on a small but fully heterogeneous MPI platform. Our results show the superiority of those heuristics which fully take into account the relative capacity of the communication links. [Copyright &y& Elsevier]

This paper considers steady-state scheduling techniques for heterogeneous systems, such as clusters and grids. The use of steady-state scheduling is advocated to solve a variety of important problems, which would be too difficult to tackle with the objective of makespan minimization. Several examples are given, namely master-slave tasking, mixed task and data parallelism, and pipelined macro-communications (scatter, broadcast, multicast). For each example, both the advantages and the limitations of the approach are discussed. [ABSTRACT FROM AUTHOR]