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The paper explains why Amdahl's Law shall be interpreted specifically for distributed parallel systems and why it generated so many debates, discussions, and abuses. We set up a general model and list many of the terms affecting parallel…

In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the…

With the spread of multi- and many-core processors more and more typical task is to re-implement some source code written originally for a single processor to run on more than one cores. Since it is a serious investment, it is important to…

The modification of Amdahl's law for the case of increment of processor elements in a computer system is considered. The coefficient $k$ linking accelerations of parallel and parallel specialized computer systems is determined. The limiting…

Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description…

Classical Amdahl's Law conceptualized the limit of speedup for an era of fixed serial-parallel decomposition and homogeneous replication. Modern heterogeneous systems need a different conceptual framework: constrained resources must be…

The problem of learning parallel computer performance is investigated in the context of multicore processors. Given a fixed workload, the effect of varying system configuration on performance is sought. Conventionally, the performance…

Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this…

After Amdahl's trailblazing work, many other authors proposed analytical speedup models but none have considered the limiting effect of the memory wall. These models exploited aspects such as problem-size variation, memory size,…

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…

A parallel program can be represented as a directed acyclic graph. An important performance bound is the time to execute the critical path through the graph. We show how this performance metric is related to Amdahl speedup and the degree of…

In high performance computing environments, we observe an ongoing increase in the available numbers of cores. This development calls for re-emphasizing performance (scalability) analysis and speedup laws as suggested in the literature…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

We consider the online scheduling problem of moldable task graphs on multiprocessor systems for minimizing the overall completion time (or makespan). Moldable job scheduling has been widely studied in the literature, in particular when…

In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…

Control parallelism and data parallelism is mostly reasoned and optimized as separate functions. Because of this, workloads that are irregular, fine-grain and dynamic such as dynamic graph processing become very hard to scale. An…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a…

A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of…

In the world of supercomputers, the large number of processors requires to minimize the inefficiencies of parallelization, which appear as a sequential part of the program from the point of view of Amdahl's law. The recently suggested new…