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Henning Meyerhenke

Publications and source records attributed to Henning Meyerhenke.

At least 19 recordsLinked to original sources

Carbon-Aware Mapping and Scheduling for Deadline-Constrained Workflows

As datacenters continue to grow in scale, their energy consumption and resulting carbon footprint have become pressing concerns. With the increasing share of renewable energy in a datacenter's mixed energy supply, shifting task execution to periods of high green-power availability is a promising strategy to reduce carbon emissions. However, in heterogeneous computing environments, the power consumption of compute nodes in a datacenter can also vary. In practice, workloads submitted to datacenters are often not isolated tasks, but entire workflows consisting of interdependent tasks with precedence constraints. A further challenge arises from the fact that carbon emission reductions must typically be achieved under strict workflow deadlines. In this work, we show that the problem posed by these challenges for the scheduler is NP-hard and admits no constant-factor approximation even for the uni-processor case. Motivated by this hardness, we present a novel algorithm CWM that combines carbon-aware mapping and scheduling to construct feasible solutions. Our approach integrates dynamic programming with efficient heuristics to exploit renewable energy availability and infrastructure heterogeneity. To assess the quality of the new algorithm, we evaluate it against the state-of-the-art approach CaWoSched and show that CWM achieves significant reductions in terms of carbon emissions in experiments. In particular, we are able to achieve a median carbon cost reduction of 42% over the best version of CaWoSched when the deadline is two times the makespan of a carbon-agnostic baseline. Note that CaWoSched itself already reduces the carbon-agnostic baseline by 36%.

cs.DC

Methodology of Algorithm Engineering

Research on algorithms has drastically increased in recent years. Various sub-disciplines of computer science investigate algorithms according to different objectives and standards. This plurality of the field has led to various methodological advances that have not yet been transferred to neighboring sub-disciplines. The central roadblock for a better knowledge exchange is the lack of a common methodological framework integrating the perspectives of these sub-disciplines. It is the objective of this paper to develop a research framework for algorithm engineering. Our framework builds on three areas discussed in the philosophy of science: ontology, epistemology and methodology. In essence, ontology describes algorithm engineering as being concerned with algorithmic problems, algorithmic tasks, algorithm designs and algorithm implementations. Epistemology describes the body of knowledge of algorithm engineering as a collection of prescriptive and descriptive knowledge, residing in World 3 of Popper's Three Worlds model. Methodology refers to the steps how we can systematically enhance our knowledge of specific algorithms. The framework helps us to identify and discuss various validity concerns relevant to any algorithm engineering contribution. In this way, our framework has important implications for researching algorithms in various areas of computer science.

cs.DS

Carbon-Aware Workflow Scheduling with Fixed Mapping and Deadline Constraint

Large data and computing centers consume a significant share of the world's energy consumption. A prominent subset of the workloads in such centers are workflows with interdependent tasks, usually represented as directed acyclic graphs (DAGs). To reduce the carbon emissions resulting from executing such workflows in centers with a mixed (renewable and non-renewable) energy supply, it is advisable to move task executions to time intervals with sufficient green energy when possible. To this end, we formalize the above problem as a scheduling problem with a given mapping and ordering of the tasks. We show that this problem can be solved in polynomial time in the uniprocessor case. For at least two processors, however, the problem becomes NP-hard. Hence, we propose a heuristic framework called CaWoSched that combines several greedy approaches with local search. To assess the 16 heuristics resulting from different combinations, we also devise a simple baseline algorithm and an exact ILP-based solution. Our experimental results show that our heuristics provide significant savings in carbon emissions compared to the baseline.

cs.DC

Predicting the Performance of Scientific Workflow Tasks for Cluster Resource Management: An Overview of the State of the Art

Scientific workflow management systems support large-scale data analysis on cluster infrastructures. For this, they interact with resource managers which schedule workflow tasks onto cluster nodes. In addition to workflow task descriptions, resource managers rely on task performance estimates such as main memory consumption and runtime to efficiently manage cluster resources. Such performance estimates should be automated, as user-based task performance estimates are error-prone. In this book chapter, we describe key characteristics of methods for workflow task runtime and memory prediction, provide an overview and a detailed comparison of state-of-the-art methods from the literature, and discuss how workflow task performance prediction is useful for scheduling, energy-efficient and carbon-aware computing, and cost prediction.

cs.DC

Memory-aware Adaptive Scheduling of Scientific Workflows on Heterogeneous Architectures

The analysis of massive scientific data often happens in the form of workflows with interdependent tasks. When such a scientific workflow needs to be scheduled on a parallel or distributed system, one usually represents the workflow as a directed acyclic graph (DAG). The vertices of the DAG represent the tasks, while its edges model the dependencies between the tasks (data to be communicated to successor tasks). When executed, each task requires a certain amount of memory and if it exceeds the available memory, the execution fails. The typical goal is to execute the workflow without failures (satisfying the memory constraints) and with the shortest possible execution time (minimize its makespan). To address this problem, we investigate the memory-aware scheduling of DAG-shaped workflows on heterogeneous platforms, where each processor can have a different speed and a different memory size. We propose a variant of HEFT (Heterogeneous Earliest Finish Time) that accounts for memory and includes eviction strategies for cases when it might be beneficial to remove some data from memory in order to have enough memory to execute other tasks. Furthermore, while HEFT assumes perfect knowledge of the execution time and memory usage of each task, the actual values might differ upon execution. Thus, we propose an adaptive scheduling strategy, where a schedule is recomputed when there has been a significant variation in terms of execution time or memory. The scheduler has been integrated with a runtime system, allowing us to perform a thorough experimental evaluation on real-world workflows. The runtime system warns the scheduler when the task parameters change, so a schedule is recomputed on the fly. The memory-aware strategy allows us to schedule task graphs that would run out of memory with a state-of-the-art scheduler, and the adaptive setting allows us to significantly reduce the makespan.

cs.DC

A Fully-dynamic Approximation Algorithm for Maximum Weight b-Matchings in Graphs

Matching nodes in a graph G = (V, E) is a well-studied algorithmic problem with many applications. The b-matching problem is a generalizati on that allows to match a node with up to b neighbors. This allows more flexible connectivity patterns whenever vertices may have multiple associations. The algorithm b-suitor [Khan et al., SISC2016] is able to compute a (1/2)-approximation of a maximum weight b-matching in O(|E|) time. Since real-world graphs often change over time, fast dynamic methods for b-matching optimization are desirable. In this work, we propose Dyn-b-suitor, a dynamic algorithm for the weighted b-matching problem. As a non-trivial extension to the dynamic Suitor algorithm for 1-matchings [Angriman et al., JEA 2022], our approach computes (1/2)-approximate b-matchings by identifying and updating affected vertices without static recomputation. Our proposed algorithm is fully-dynamic, i. e., it supports both edge insertions and deletions, and we prove that it computes the same solution as its static counterpart. In extensive experiments on real-world benchmark graphs and generated instances, our dynamic algorithm yields significant savings compared to the sequential b-suitor, e. g., for batch updates with $10^3$ edges with an average acceleration factor of $10^3$. When comparing our sequential dynamic algorithm with the parallel (static) b-suitor on a 128-core machine, our dynamic algorithm is still $59$x to $10^4$ faster.

cs.DS

Introducing Total Harmonic Resistance for Graph Robustness under Edge Deletions

Assessing and improving the robustness of a graph $G$ are critical steps in network design and analysis. To this end, we consider the optimisation problem of removing $k$ edges from $G$ such that the resulting graph has minimal robustness, simulating attacks or failures. In this paper, we propose total harmonic resistance as a new robustness measure for this purpose - and compare it to the recently proposed forest index [Zhu et al., IEEE Trans.\ Inf.\ Forensics and Security, 2023]. Both measures are related to the established total effective resistance measure, but their advantage is that they can handle disconnected graphs. This is also important for originally connected graphs due to the removal of the $k$ edges. To compare our measure with the forest index, we first investigate exact solutions for small examples. The best $k$ edges to select when optimizing for the forest index lie at the periphery. Our proposed measure, in turn, prioritizes more central edges, which should be beneficial for most applications. Furthermore, we adapt a generic greedy algorithm to our optimization problem with the total harmonic resistance. With this algorithm, we perform a case study on the Berlin road network and also apply the algorithm to established benchmark graphs. The results are similar as for the small example graphs above and indicate the higher suitability of the new measure.

cs.SI

Mapping Large Memory-constrained Workflows onto Heterogeneous Platforms

Scientific workflows are often represented as directed acyclic graphs (DAGs), where vertices correspond to tasks and edges represent the dependencies between them. Since these graphs are often large in both the number of tasks and their resource requirements, it is important to schedule them efficiently on parallel or distributed compute systems. Typically, each task requires a certain amount of memory to be executed and needs to communicate data to its successor tasks. The goal is thus to execute the workflow as fast as possible (i.e., to minimize its makespan) while satisfying the memory constraints. Hence, we investigate the partitioning and mapping of DAG-shaped workflows onto heterogeneous platforms where each processor can have a different speed and a different memory size. We first propose a baseline algorithm in the absence of existing memory-aware solutions. As our main contribution, we then present a four-step heuristic. Its first step is to partition the input DAG into smaller blocks with an existing DAG partitioner. The next two steps adapt the resulting blocks of the DAG to fit the processor memories and optimize for the overall makespan by further splitting and merging these blocks. Finally, we use local search via block swaps to further improve the makespan. Our experimental evaluation on real-world and simulated workflows with up to 30,000 tasks shows that exploiting the heterogeneity with the four-step heuristic reduces the makespan by a factor of 2.44 on average (even more on large workflows), compared to the baseline that ignores heterogeneity.

cs.DC

Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc-bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

cs.DC

Greedy Optimization of Resistance-based Graph Robustness with Global and Local Edge Insertions

The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective resistance (i.e., is most robust) -- one where the new edges can be anywhere in the graph and one where the new edges need to be incident to a specified focus node. The total effective resistance and effective resistances between nodes can be computed using the pseudoinverse of the graph Laplacian. The pseudoinverse may be computed explicitly via pseudoinversion; yet, this takes cubic time in practice and quadratic space. We instead exploit combinatorial and algebraic connections to speed up gain computations in an established generic greedy heuristic. Moreover, we leverage existing randomized techniques to boost the performance of our approaches by introducing a sub-sampling step. Our different graph- and matrix-based approaches are indeed significantly faster than the state-of-the-art greedy algorithm, while their quality remains reasonably high and is often quite close. Our experiments show that we can now process larger graphs for which the application of the state-of-the-art greedy approach was impractical before.

cs.SI

Network Sparsification via Degree- and Subgraph-based Edge Sampling

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with filtering-based edge sampling being the most typical one, heavily relies on an appropriate definition of edge importance. Instead, we propose a different perspective with a generalized local-property-based sampling method, which preserves (scaled) local \emph{node} characteristics. Apart from degrees, these local node characteristics we use are the expected (scaled) number of wedges and triangles a node belongs to. Through such a preservation, main complex structural properties are preserved implicitly. We adapt a game-theoretic framework from uncertain graph sampling by including a threshold for faster convergence (at least $4$ times faster empirically) to approximate solutions. Extensive experimental studies on functional climate networks show the effectiveness of this method in preserving macroscopic to mesoscopic and microscopic network structural properties.

cs.SI

Algorithms for Large-scale Network Analysis and the NetworKit Toolkit

The abundance of massive network data in a plethora of applications makes scalable analysis algorithms and software tools necessary to generate knowledge from such data in reasonable time. Addressing scalability as well as other requirements such as good usability and a rich feature set, the open-source software NetworKit has established itself as a popular tool for large-scale network analysis. This chapter provides a brief overview of the contributions to NetworKit made by the DFG Priority Programme SPP 1736 Algorithms for Big Data. Algorithmic contributions in the areas of centrality computations, community detection, and sparsification are in the focus, but we also mention several other aspects -- such as current software engineering principles of the project and ways to visualize network data within a NetworKit-based workflow.

cs.SI

More Recent Advances in (Hyper)Graph Partitioning

In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic. In particular, the survey extends the previous survey by also covering hypergraph partitioning and streaming algorithms, and has an additional focus on parallel algorithms.

cs.DS

Fast Dynamic Updates and Dynamic SpGEMM on MPI-Distributed Graphs

Sparse matrix multiplication (SpGEMM) is a fundamental kernel used in many diverse application areas, both numerical and discrete. For example, many algebraic graph algorithms rely on SpGEMM in the tropical semiring to compute shortest paths in graphs. Recently, SpGEMM has received growing attention regarding implementations for specific (parallel) architectures. Yet, this concerns only the static problem, where both input matrices do not change. In many applications, however, matrices (or their corresponding graphs) change over time. Although recomputing from scratch is very expensive, we are not aware of any dynamic SpGEMM algorithms in the literature. In this paper, we thus propose a batch-dynamic algorithm for MPI-based parallel computing. Building on top of a distributed graph/matrix data structure that allows for fast updates, our dynamic SpGEMM reduces the communication volume significantly. It does so by exploiting that updates change far fewer matrix entries than there are non-zeros in the input operands. Our experiments with popular benchmark graphs show that our approach pays off. For batches of insertions or removals of matrix entries, our dynamic SpGEMM is substantially faster than the static algorithms in the state-of-the-art competitors CombBLAS, CTF and PETSc.

cs.DC

Interactive Visualization of Protein RINs using NetworKit in the Cloud

Network analysis has been applied in diverse application domains. In this paper, we consider an example from protein dynamics, specifically residue interaction networks (RINs). In this context, we use NetworKit -- an established package for network analysis -- to build a cloud-based environment that enables domain scientists to run their visualization and analysis workflows on large compute servers, without requiring extensive programming and/or system administration knowledge. To demonstrate the versatility of this approach, we use it to build a custom Jupyter-based widget for RIN visualization. In contrast to existing RIN visualization approaches, our widget can easily be customized through simple modifications of Python code, while both supporting a good feature set and providing near real-time speed. It is also easily integrated into analysis pipelines (e.g., that use Python to feed RIN data into downstream machine learning tasks).

cs.SI

Tarema: Adaptive Resource Allocation for Scalable Scientific Workflows in Heterogeneous Clusters

Scientific workflow management systems like Nextflow support large-scale data analysis by abstracting away the details of scientific workflows. In these systems, workflows consist of several abstract tasks, of which instances are run in parallel and transform input partitions into output partitions. Resource managers like Kubernetes execute such workflow tasks on cluster infrastructures. However, these resource managers only consider the number of CPUs and the amount of available memory when assigning tasks to resources; they do not consider hardware differences beyond these numbers, while computational speed and memory access rates can differ significantly. We propose Tarema, a system for allocating task instances to heterogeneous cluster resources during the execution of scalable scientific workflows. First, Tarema profiles the available infrastructure with a set of benchmark programs and groups cluster nodes with similar performance. Second, Tarema uses online monitoring data of tasks, assigning labels to tasks depending on their resource usage. Third, Tarema uses the node groups and task labels to dynamically assign task instances evenly to resources based on resource demand. Our evaluation of a prototype implementation for Kubernetes, using five real-world Nextflow workflows from the popular nf-core framework and two 15-node clusters consisting of different virtual machines, shows a mean reduction of isolated job runtimes by 19.8% compared to popular schedulers in widely-used resource managers and 4.54% compared to the heuristic SJFN, while providing a better cluster usage. Moreover, executing two long-running workflows in parallel and on restricted resources shows that Tarema is able to reduce the runtimes even more while providing a fair cluster usage.

cs.DC

The climatic interdependence of extreme-rainfall events around the globe

The identification of regions of similar climatological behavior can be utilized for the discovery of spatial relationships over long-range scales, including teleconnections. In this regard, the global picture of the interdependence patterns of extreme rainfall events (EREs) still needs to be further explored. To this end, we propose a top-down complex-network-based clustering workflow, with the combination of consensus clustering and mutual correspondences. Consensus clustering provides a reliable community structure under each dataset, while mutual correspondences build a matching relationship between different community structures obtained from different datasets. This approach ensures the robustness of the identified structures when multiple datasets are available. By applying it simultaneously to two satellite-derived precipitation datasets, we identify consistent synchronized structures of EREs around the globe, during boreal summer. Two of them show independent spatiotemporal characteristics, uncovering the primary compositions of different monsoon systems. They explicitly manifest the primary intraseasonal variability in the context of the global monsoon, in particular the `monsoon jump' over both East Asia and West Africa and the mid-summer drought over Central America and southern Mexico. Through a case study related to the Asian summer monsoon (ASM), we verify that the intraseasonal changes of upper-level atmospheric conditions are preserved by significant connections within the global synchronization structure. Our work advances network-based clustering methodology for (i) decoding the spatiotemporal configuration of interdependence patterns of natural variability and for (ii) the intercomparison of these patterns, especially regarding their spatial distributions over different datasets.

physics.ao-ph

An MPI-based Algorithm for Mapping Complex Networks onto Hierarchical Architectures

Processing massive application graphs on distributed memory systems requires to map the graphs onto the system's processing elements (PEs). This task becomes all the more important when PEs have non-uniform communication costs or the input is highly irregular. Typically, mapping is addressed using partitioning, in a two-step approach or an integrated one. Parallel partitioning tools do exist; yet, corresponding mapping algorithms or their public implementations all have major sequential parts or other severe scaling limitations. In this paper, we propose a parallel algorithm that maps graphs onto the PEs of a hierarchical system. Our solution integrates partitioning and mapping; it models the system hierarchy in a concise way as an implicit labeled tree. The vertices of the application graph are labeled as well, and these vertex labels induce the mapping. The mapping optimization follows the basic idea of parallel label propagation, but we tailor the gain computations of label changes to quickly account for the induced communication costs. Our MPI-based code is the first public implementation of a parallel graph mapping algorithm; to this end, we extend the partitioning library ParHIP. To evaluate our algorithm's implementation, we perform comparative experiments with complex networks in the million- and billion-scale range. In general our mapping tool shows good scalability on up to a few thousand PEs. Compared to other MPI-based competitors, our algorithm achieves the best speed to quality trade-off and our quality results are even better than non-parallel mapping tools.

cs.DC