Network Flows

Ahuja, R. K., Magnanti, & Orlin, J. B. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice Hall.

Type

Book

Intellectual base

Textbook

Year

1993

Link

https://www.pearson.com/en-us/subject-catalog/p/Ahuja-Network-Flows-Theory-Algorithms-and-Applications/P200000003456/9780136175490

Cited from

operations_research

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Network Flow Models
  • The tooling ecosystem is broad: network-flow algorithms in general-purpose LP solvers (CPLEX, Gurobi, HiGHS, all with network-flow specializations); specialized libraries (LEMON graph library in C++; NetworkX and OR-Tools in Python; JuliaGraphs ecosystem); graph-database and graph-processing frameworks (Neo4j for storage with graph-algorithm libraries; Apache Giraph, Spark GraphX for distributed graph processing); and mature academic references (Ahuja, Magnanti, and Orlin (1993) as the canonical network-flow textbook; Goldberg-Tarjan and others for algorithm-specific literature).

Domain-specific

• Closure problem
  • A closure of a directed graph contains every successor of each selected vertex; the maximum-closure problem asks for a closure maximizing the sum of vertex weights.
• Minimum-cost flow problem
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Multi-commodity flow problem
  • A multi-commodity flow problem assigns a separate conserved flow to every commodity while constraining the sum of their edge loads by shared capacities and optimizing a declared objective.
• Network Simplex Algorithm
  • This is more precise than saying that every nonbasic arc is zero; upper-bound nonbasic arcs are essential in capacitated formulations.

    This sourceChapter 11 treats network-simplex algorithms, tree solutions, potentials, pivot rules, sensitivity, and their relationship to general simplex.

Verification

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