A Multi-Threading Algorithm to Detect and Remove Cycles in Vertex- and Arc-Weighted Digraph

Cui, Huanqing; Niu, Junfeng; Zhou, Chuanai; Shu, Minglei

doi:10.3390/a10040115

“…Parallel and distributed algorithms for cycle enumeration. Cui et al [13] proposed a multi-threaded algorithm for detecting and removing simple cycles of a directed graph. The algorithm divides the graph into its strongly-connected components and each thread performs a depth-first search on a different component to find cycles.…”

Section: Related Workmentioning

confidence: 99%

Scalable Fine-Grained Parallel Cycle Enumeration Algorithms

Blanuša,

Ienne,

Atasu

2022

Preprint

0

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This paper investigates scalable parallelisation of state-of-the-art cycle enumeration algorithms by Johnson and Read-Tarjan along with their applications to temporal graphs. We provide a comprehensive theoretical analysis of various parallel versions of these algorithms and evaluate their performance on multi-core processors. We show that a straightforward coarse-grained parallelisation approach is not scalable and suffers from load imbalance issues. To eliminate the load imbalance, we modify the Johnson and the Read-Tarjan algorithms to exploit finer-grained parallelism. We show that our fine-grained parallel Read-Tarjan algorithm is theoretically work efficient-i.e., it does no more work than its serial version. However, our fine-grained parallel Johnson algorithm does not share this property. Yet, in practice, our fine-grained parallel Johnson algorithm outperforms our fine-grained parallel Read-Tarjan algorithm. In any case, both of our contributed fine-grained parallel algorithms are scalable, meaning that they can effectively utilise an increasing number of software threads, which we prove theoretically and demonstrate through extensive experiments. On a cluster of multi-core CPUs with 256 physical cores that can execute 1024 simultaneous threads, our fine-grained parallel Johnson and Read-Tarjan algorithms are respectively up to 435× and 470× faster than their single-threaded versions. On the same compute cluster, our fine-grained parallel algorithms are on average an order of magnitude faster than their coarse-grained parallel counterparts.

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“…The problem of cycle elimination from directed graphs to get an acyclic graph is a wellstudied area in graph theory. An overview of graph cycles is provided by Kavitha et al (2009), and a fast parallel algorithm for finding the cycles in a graph is proposed in Cui et al (2017). Here, we develop our own method, starting with the concept of "weight".…”

Section: Finding the Maximum-weight Set Of Cyclesmentioning

confidence: 99%

Mathematical Foundations for Balancing the Payment System in the Trade Credit Market

Fleischman¹,

Dini

²

2021

JRFM

2

0

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The increasingly complex economic and financial environment in which we live makes the management of liquidity in payment systems and the economy in general a persistent challenge. New technologies make it possible to address this challenge through alternative solutions that complement and strengthen existing payment systems. For example, interbank balancing and clearing methods (such as real-time gross settlement) can also be applied to private payments, complementary currencies, and trade credit clearing to provide better liquidity and risk management. The paper defines the concept of a balanced payment system mathematically and demonstrates the effects of balancing on a few small examples. It then derives the construction of a balanced payment subsystem that can be settled in full and therefore that can be removed in toto to achieve debt reduction and payment gridlock resolution. Using well-known results from graph theory, the main output of the paper is the proof—for the general formulation of a payment system with an arbitrary number of liquidity sources—that the amount of liquidity saved is maximum, along with a detailed discussion of the practical steps that a lending institution can take to provide different levels of service subject to the constraints of available liquidity and its own cap on total overdraft exposure. From an applied mathematics point of view, the original contribution of the paper is two-fold: (1) the introduction of a liquidity node with a store of value function in obligation-clearing; and (2) the demonstration that the case with one or more liquidity sources can be solved with the same mathematical machinery that is used for obligation-clearing without liquidity. The clearing and balancing methods presented are based on the experience of a specific application (Tetris Core Technologies), whose wider adoption in the trade credit market could contribute to the financial stability of the whole economy and a better management of liquidity and risk overall.

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“…The problem of cycle elimination from directed graphs to get an acyclic graph is a well-studied area in graph theory. An overview of cycles in a graph is provided by [5], and a fast parallel algorithm for finding the cycles in a graph is proposed in [6]. Here we develop our own method, starting with the concept of "weight".…”

Section: Finding the Maximum-weight Set Of Cyclesmentioning

confidence: 99%

Balancing the Payment System

Fleischman¹,

Dini²

2020

Preprint

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The increasingly complex economic and financial environment in which we live makes the management of liquidity in payment systems and the economy in general a persistent challenge. New technologies are making it possible to address this challenge through alternative solutions that complement and strengthen existing payment systems. For example, the interbank balancing method can also be applied to private payment systems, complementary currencies, and trade credit clearing systems to provide better liquidity and risk management. In this paper we introduce the concept of a balanced payment system and demonstrate the effects of balancing on a small example. We show how to construct a balanced payment subsystem that can be settled in full and, therefore, that can be removed from the payment system to achieve liquidity-saving and payments gridlock resolution. We also briefly introduce a generalization of a payment system and of the method to balance it in the form of a specific application (Tetris Core Technologies), whose wider adoption could contribute to the financial stability of and better management of liquidity and risk for the whole economy.

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A Multi-Threading Algorithm to Detect and Remove Cycles in Vertex- and Arc-Weighted Digraph

Cited by 8 publications

References 19 publications

Scalable Fine-Grained Parallel Cycle Enumeration Algorithms

Scalable Fine-Grained Parallel Cycle Enumeration Algorithms

Mathematical Foundations for Balancing the Payment System in the Trade Credit Market

Balancing the Payment System

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