What is Hungarian matching algorithm?

The Hungarian matching algorithm, also called the Kuhn-Munkres algorithm, is a O ( ∣ V ∣ 3 ) O\big(|V|^3\big) O(∣V∣3) algorithm that can be used to find maximum-weight matchings in bipartite graphs, which is sometimes called the assignment problem. This can also be adapted to find the minimum-weight matching.

How is the Hungarian algorithm used?

Then the steps of the Hungarian Algorithm are as follows:

1. Subtract row minima.
2. Subtract column minima.
3. Cover all zeros with the minimum number of lines.
4. Create additional zeros by finding the smallest element – call it c – that isn’t covered by a line.

What is the logic in Hungarian algorithm?

The cost of each perfect matching is at least the value of each potential: the total cost of the matching is the sum of costs of all edges; the cost of each edge is at least the sum of potentials of its endpoints; since the matching is perfect, each vertex is an endpoint of exactly one edge; hence the total cost is at …

Is Hungarian algorithm greedy?

It can be solved optimally by the Hungarian algorithm in O(n^3). However, let us consider the following suboptimal greedy algorithm: Choose the maximal element in the remaining matrix. Add this element to the resulting set, i.e. match the row of this element to its column, and remove these row and column from the …

Why the Hungarian method gives an optimal solution?

This was named the Hungarian method. This method was capable of reducing the cost matrix such that at least one zero in each row and column will be obtained; thus optimal assignment will be made possible where opportunity cost is zero.

Is Hungarian algorithm optimal?

Since S was arbitrary, it follows that for every optimal solution to the original problem, the Hungarian algorithm is capable of finding it, depending on how it breaks ties. This is a sense in which the Hungarian algorithm finds all optimal solutions.

How is the Hungarian method an assignment problem?

To solve the problem we have to perform the following steps:

1. Step 1 – Subtract the row minimum from each row.
2. Step 2 – Subtract the column minimum from each column from the reduced matrix.
3. Step 3 – Assign one “0” to each row & column.