Improved Algorithm for the Incremental Assignment Problem

10 pages•Published: June 9, 2021

Pinzhi Wang, Youssou Gningue and Haibin Zhu

Abstract

The Assignment Problem is a basic combinatorial optimization problem. In a weighted bipartite graph, the Assignment Problem is to find the largest sum of weights matching. The Hungarian method is a well-known algorithm, which is combinatorial optimization. Adding a new row and a new column to a weighted bipartite graph is called the Incremental Assignment Problem (IAP). The algorithm of the Incremental Assignment Problem utilizes the given optimal solution (the maximum weighted matching) and the dual variables to solve the matrix after extending the bipartite graph. This paper proposes an improvement of the Incremental Assignment Algorithm (IAA), named the Improved Incremental Assignment Algorithm (IIAA). The improved algorithm will save the operation time and operation space to find the optimal solution (the maximum weighted matching) of the bipartite graph.

Keyphrases: assignment problem, hungarian algorithm, incremental assignment problem, weighted bipartite graph

In: Yan Shi, Gongzhu Hu, Takaaki Goto and Quan Yuan (editors). CAINE 2020. The 33rd International Conference on Computer Applications in Industry and Engineering, vol 75, pages 98-107.

Links:	https://easychair.org/publications/paper/f27r
	https://doi.org/10.29007/8d9g

BibTeX entry

@inproceedings{CAINE2020:Improved_Algorithm_Incremental_Assignment,
  author    = {Pinzhi Wang and Youssou Gningue and Haibin Zhu},
  title     = {Improved Algorithm for  the Incremental Assignment Problem},
  booktitle = {CAINE 2020. The 33rd International Conference on Computer Applications  in Industry and Engineering},
  editor    = {Yan Shi and Gongzhu Hu and Takaaki Goto and Quan Yuan},
  series    = {EPiC Series in Computing},
  volume    = {75},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/f27r},
  doi       = {10.29007/8d9g},
  pages     = {98-107},
  year      = {2021}}

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