Table 3 Conclusion of literature review
Algorithms | Run time | Input | Limitations |
|---|---|---|---|
\(n \times m\) | \(n \times m\) matrix for each set of vertices (List of preferences) | – | |
\((n \times m - \min (n,m))\sqrt {n + m}\) | \(n \times m\) matrix (A unweighted bipartite graph) | Does not satisfy assumption 2 and 1 | |
Ford-Fulkerson (Backman and Huynh 2018) | \((n \times m - \min (n,m)) \times f\) | \(n \times m\) matrix (A unweighted bipartite graph) and capacity of each vertices | Does not satisfy assumption 2 |
Hungarian (Kuhn 1956) | \(\begin{gathered} (n + m)^{3} = n^{3} + m^{3} + \hfill \\ 2n^{2} m + 2nm^{2} + 1 \hfill \\ \end{gathered}\) | \(n \times m\) matrix (Cost of matching vertices) | Does not satisfy assumption 1 |
Cycle cancelling (Shepherd and Zhang 1999; Nassir et al. 2014) | \((n \times m - \min (n,m)) \times C \times U\) | \(n \times m\) matrix (Cost of matching vertices) and capacity and supply/demand of vertices | – |
\(\begin{gathered} (n + m)(n \times m - \min (n,m)) \hfill \\ \log (n + m)\log ((n + m)C) \hfill \\ \end{gathered}\) | \(n \times m\) matrix (Cost of matching vertices) | Does not satisfy assumption 1 |