The partitioning technique of directed cyclic graph for task assignment problem

Ariffin, Wan Nor Munirah; Salleh, Shaharuddin

doi:10.1063/1.4954523

Cited by 4 publications

(3 citation statements)

References 5 publications

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“…Other algorithms developed to analyze these types of networks include MapReduce (Dean and Ghemawat 2008) and PowerGraph (Gonzalez et al 2012). Further attention has been given to this topic at conferences hosted by companies like Google and IBM (Ariffin and Salleh 2016;Aydin et al 2016;Bourse et al 2014;Gupta 1997;Mokashi and Kulkarni 2018). Many of these algorithms leverage a scale-free power-law relationship in node connections, which is a reasonable proxy for many information networks (Barabasi and Albert 1999;Zhang et al 2011).…”

Section: Power-law Connectivitymentioning

confidence: 99%

A Topological Approach to Partitioning Flow Networks for Parallel Simulation

Tiernan

Hodges

2022

J. Comput. Civ. Eng.

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System partitioning for effective simulation of civil infrastructure flow networks on parallel processors is a non-trivial problem. Arbitrary partitioning focused only on balancing processor workload can lead to a large inter-processor communication burden that limits parallel speedup. Thus, there is a need for intelligent partitioning algorithms that balance the estimated computational load while minimizing the number of connections between partitions. Graph Theory provides widely-used partitioning methods, but these are applicable to networks with power-law connectivity and where the computational workload is proportional to the number of system nodes -conditions that do not hold for finite-volume solution of water drainage networks (e.g. river systems, stormwater drainage systems). This paper presents the novel "BIPquick" algorithm, which is shown to be an effective approach to identifying network partitions with reduced connectivity for systems that are Directed Acyclic Graphs (DAG) and have a physical limit on the number of connections per network node.Novel developments include (i) a "node-cut" approach that allows a partitioning workload function to be exactly balanced in systems where the computational work is proportional to the link length between nodes, (ii) a finite-pass approach to partitioning that ensures a partitioning solution in a known time, and (iii) a new connectivity scaling metric that allows simple evaluation and comparison of different partitioning results. The BIPquick model is tested on a large river network with up to 10,000 partitions. Tiernan, March 21, 2022 limited to junctions with less than 10 connecting links. Thus, practical approaches to the partitioning networks with limited junction connectivity are of interest to civil engineering.To further limit our scope, in finite-volume, unsteady flow models in a network the links ("edges" in Graph Theory) between nodes are subdivided into smaller elements of roughly uniform size such that the computational work scales on the link lengths -which contrasts with traditional link-node models (e.g., EPANET, SWMM) where the link length does not directly affect the workload. Hence, we focus herein on partitioning with link-dependent load balancing for gravity-drainage networks solved with finite-volume algorithms.As a simple example of the importance of both inter-processor communication and workload in partitioning, consider a network with N links of uniform length partitioned onto K processors where N ≫ K. The workload on an individual processor is (in this case) the number of links assigned to the processor. The overall communication burden is the number of nodes that connect to more than one processor. Figure 1a illustrates a worst-case condition for communication by using random sort, i.e. link-balance partitioning of an unsorted set. The random sort achieves workload balance, but at the cost of the inter-processor communication load scaling on N . In contrast, Fig. 1(b) illustrates, the reverse problem, a partitioning scheme that minimi...

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Section: Power-law Connectivitymentioning

confidence: 99%

A Topological Approach to Partitioning Flow Networks for Parallel Simulation

Tiernan

Hodges

2022

J. Comput. Civ. Eng.

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“…In DAGs interdependencies between variables are directed and the causal flow has topological ordering such that it does not loop back to form a cycle. While there have been attempts to reduce directed cyclic graphs (DCGs) to DAGs, not all systems can be satisfactorily modeled as DAGs, for instance, those in social sciences, economics, and incidentally SSRFBs. Open questions at this juncture include whether causality can be discovered in a DCG at all, if the DCG in question can be satisfactorily reduced to a DAG, and what kind of information would be lost or misinterpreted through this assumption.…”

Section: Introductionmentioning

confidence: 99%

Handling Complexity of Semisolid Redox Flow Battery Operation Principles through Mechanistic Simulations

Shukla

Franco

2018

J. Phys. Chem. C

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In this paper, the semisolid redox flow battery (SSRFB) in static mode is investigated through a kinetic Monte Carlo-based mechanistic model. Electrochemical reactions are said to occur in particle suspensions composed of carbon as conductive additive and silicon as active material, where silicon is known to undergo volume expansion on discharge. The coexistence of different physical phenomena in suspension is not trivial and leads to complex behavior. This work attempts to quantify physical complexity through parameter sensitivity analysis and some basic tools of graph theory. The systematic treatment employed herein not only expands the utility of mechanistic models, but also provides a more comprehensive theoretical understanding of these complex systems which can otherwise only be treated as black boxes. It is concluded that the primary source of complexity of the SSRFB is the competition between multiple phenomena and that quantifying the dynamics between parameters is as important as measuring a specific parameter. A systematic method of studying the dynamics is to compartmentalize the complex system by introduction of mesoscopic parameters that emerge as a result of contributing microscale phenomena.

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“…Ariffin and Salleh [9] put an effort to reduce the graph onto directed acyclic graph. A Kernighan-Lin algorithm is applied to obtain the partition of tasks.…”

Section: Introductionmentioning

confidence: 99%

The Reduction of Directed Cyclic Graph for Task Assignment Problem

Ariffin

2018

MATEC Web of Conferences

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In this paper, a directed cyclic graph (DCG) is proposed as the task graph. It is undesirable and impossible to complete the task according to the constraints if the cycle exists. Therefore, an effort should be done in order to eliminate the cycle to obtain a directed acyclic graph (DAG), so that the minimum amount of time required for the entire task can be found. The technique of reducing the complexity of the directed cyclic graph to a directed acyclic graph by reversing the orientation of the path is the main contribution of this study. The algorithm was coded using Java programming and consistently produced good assignment and task schedule.

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The partitioning technique of directed cyclic graph for task assignment problem

Cited by 4 publications

References 5 publications

A Topological Approach to Partitioning Flow Networks for Parallel Simulation

A Topological Approach to Partitioning Flow Networks for Parallel Simulation

Handling Complexity of Semisolid Redox Flow Battery Operation Principles through Mechanistic Simulations

The Reduction of Directed Cyclic Graph for Task Assignment Problem

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