Modified EDMONDS-KARP Algorithm to Solve Maximum Flow Problems

Mallick, Kalyan Kumar; Khan, Aminur Rahman; Ahmed, Mollah Mesbahuddin; Uddin, Md. Sharif

doi:10.4236/ojapps.2016.62014

Cited by 14 publications

(8 citation statements)

References 10 publications

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“…The weight of an edge represents the number of reference genes supporting the “connection” of two nodes. To assemble fragmented transcripts into longer sequences, TransMCL applies a net‐flow model to discover multiple paths, each representing a connection of a series of fragmented transcripts from the 5′ end to the 3′ end, by maximizing the summary of flow through the whole graph based on the Edmonds‐Karp strategy (Mallick et al, 2016). The algorithm utilizes the concept of augmenting paths to iteratively enhance the flow in the network until the maximum possible flow is achieved.…”

Section: Methodsmentioning

confidence: 99%

TransMCL enables the assembly of full‐length coding genes for collecting complete hierarchical orthogroups

et al. 2023

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Transcriptome sequencing technologies have revolutionized the field of phylogenomics by facilitating the identification of homologous genes for species without whole genome sequences. To infer complex evolution relationship among eukaryotes, it is essential to obtain complete sequences of protein‐coding genes to provide informative mutations. However, transcriptomes in eukaryotes often consist of a large number of duplicated genes and alternative isoforms, bringing great challenges for developing effective tools to obtain complete coding gene sequences. Here, we present a net‐flow based assembler TransMCL, which aims to assemble fragmented transcripts into complete sequences while eliminating redundant isoforms during homologue clustering. By employing Markov clustering strategies and homologous gene guidance, TransMCL can accurately assemble genes for multiple organisms in an affordable time frame, making it well‐suited for phylogenomic studies based on transcriptomic data. Our results demonstrate that TransMCL can assemble 89.95%–92.95% of the total expressed genes into near‐complete transcripts on benchmark plant/animal datasets. Furthermore, applying TransMCL to multiple transcriptomes in a single run enhances the completeness of genes, even in the absence of guidance homologues from closely related species. These findings highlight the potential of TransMCL in phylogenomic studies, enabling the comprehensive characterization of gene families at the whole genome scale. By overcoming the challenges of complex gene contents in eukaryotes, TransMCL can significantly enhance our understanding of evolution of gene families across species.

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Section: Methodsmentioning

confidence: 99%

TransMCL enables the assembly of full‐length coding genes for collecting complete hierarchical orthogroups

et al. 2023

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“…Among the best known maximum flow algorithms are Ford-Fulkerson algorithm, Edmonds-Karp algorithm, King, Rao, Tarjan's (KRT) algorithm and other. This work uses a modified Edmonds-Karp (EK) algorithm to find the best path for multicast flows following the protocol described in [9]. The choice of the algorithm was motivated primarily by the faster algorithm run-time and the ready availability of software libraries implementing it.…”

Section: Dimensioning Multicast Flowsmentioning

confidence: 99%

Implementing Resource-Aware Multicast Forwarding in Software Defined Networks

Poderys

Sunny

Soler

2018

Advances in Intelligent Systems and Computing

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Using multicast data transmissions, data can be efficiently distributed to a high number of network users. However, in order to efficiently stream multimedia using multicast communication, multicast routing protocols must have knowledge of all network links and their available bandwidth. In Software Defined Networks (SDN), all this information is available in a centralized entity-SDN network. This work proposes to utilize the SDN paradigm to perform network-resources aware multicast data routing in the SDN controller. In a prototype implementation, multicast data is routed using a modified Edmonds-Karp algorithm, by taking into account network topology and links load information. This paper presents the algorithm, implementation details, and an analysis of the testing results.

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“…The fundamental TP was first proposed by F. L. Hitchcock in 1941, and then independently by T. C. Koopmans in 1947, after which the logical solution procedures from the simplex algorithm were further developed (Kulkarni & Datar, 2010;Mallick et al, 2016), primarily by Dantzig and then by Charnes et al (1953). The Simplex Method isn't reasonable for the transportation problem, especially for large scale transportation problems, in view of the interesting structure of the model by charges and Cooper (1954) who made the Stepping Stone method.…”

Section: Introductionmentioning

confidence: 99%

New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems

Ekanayake¹,

Daundasekara²,

Perera³

2022

MAS

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The maximum flow problem is also one of the highly regarded problems in the field of optimization theory in which the objective is to find a feasible flow through a flow network that obtains the maximum possible flow rate from source to sink. The literature demonstrates that different techniques have been developed in the past to handle the maximum amount of flow that the network can handle. The Ford-Fulkerson algorithm and Dinic's Algorithm are the two major algorithms for solving these types of problems. Also, the Max-Flow Min-Cut Theorem, the Scaling Algorithm, and the Push–relabel maximum flow algorithm are the most acceptable methods for finding the maximum flows in a flow network. In this novel approach, the paper develops an alternative method of finding the maximum flow between the source and target nodes of a network based on the "max-flow." Also, a new algorithmic approach to solving the transportation problem (minimizing the transportation cost) is based upon the new maximum flow algorithm. It is also to be noticed that this method requires a minimum number of iterations to achieve optimality. This study's algorithmic approach is less complicated than the well-known meta-heuristic algorithms in the literature. 

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Modified EDMONDS-KARP Algorithm to Solve Maximum Flow Problems

Cited by 14 publications

References 10 publications

TransMCL enables the assembly of full‐length coding genes for collecting complete hierarchical orthogroups

TransMCL enables the assembly of full‐length coding genes for collecting complete hierarchical orthogroups

Implementing Resource-Aware Multicast Forwarding in Software Defined Networks

New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems

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