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Note about network decomposition by maximum flow

Tianhang Lu

Abstract

The goal of this paper is to establish a decomposition of the network based on the maximum flow problem.

Note about network decomposition by maximum flow

Abstract

The goal of this paper is to establish a decomposition of the network based on the maximum flow problem.

Paper Structure

This paper contains 5 sections, 17 theorems, 16 equations, 1 figure.

Table of Contents

  1. The Maximum Flow Problems and Minimum Cut Problems
  2. Strict Complementarity Conditions
  3. Decomposition of the Network by Maximum Flow
  4. Decomposition of the Network and Minimum Cut
  5. Decomposition of Networks and Potential Functions

Key Result

Theorem 1.1

The value of the maximum $s-t$ flow in a network equals the capacity of the minimum $s-t$ cut.

Figures (1)

  • Figure 1: Three types of edges and five types of vertex sets in the network.

Theorems & Definitions (37)

  • Theorem 1.1: Max-flow min-cut theorem Ford1956maximal
  • Theorem 2.1: Strict complementarity conditions, see e.g. Sch1987theory
  • Definition 2.2
  • Definition 3.1
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • proof
  • Definition 3.4
  • Example 3.5
  • ...and 27 more