Assignment hungarian solve

assignment-hungarian-solve · version 1.0.0 · Optimization & voting · free, no key needed

Solve a bounded rectangular integer minimum-cost assignment with explicit unmatched costs.

Use when you need to: solve minimum cost assignment · run Hungarian assignment · assign rows to columns.

Decide before calling

Read the versioned contract and the supported scope below. Reuse assignment-hungarian-solve@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use assignment-hungarian-solve@1.0.0 for solve minimum cost assignment. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

solve minimum cost assignment
run Hungarian assignment
assign rows to columns
optimize rectangular matching
compute bipartite assignment
handle unmatched assignment rows
find deterministic optimal matching

Not supported

maximum-weight matching without cost conversion
capacitated or many-to-one assignment

Behavior

An r-by-c input becomes an (r+c)-square assignment: c dummy rows charge unmatched column costs, r dummy columns charge unmatched row costs, and dummy-to-dummy edges cost zero.
Among equal-cost solutions, the public row-to-column sequence is lexicographically smallest, with real columns before the null unmatched choice.
The returned total is an exact safe integer; an unsafe total is rejected instead of rounded.

Input

costs (array of array of integer, required): max items 20; each max items 20; each each min -9007199254740991; each each max 9007199254740991
unmatched_row_cost (integer, required): min -9007199254740991; max 9007199254740991
unmatched_column_cost (integer, required): min -9007199254740991; max 9007199254740991

Output

assignments (array of object, required): max items 20
unmatched_columns (array of integer, required): max items 20; each min 0; each max 19
total_cost (integer, required): min -9007199254740991; max 9007199254740991

Limits

max dimension: 20
max abs cost: 9007199254740991

Example

Request input:

{
  "costs": [
    [
      4,
      1
    ],
    [
      2,
      3
    ]
  ],
  "unmatched_row_cost": 9,
  "unmatched_column_cost": 9
}

Response:

{
  "result": {
    "assignments": [
      {
        "row": 0,
        "column": 1,
        "cost": 1
      },
      {
        "row": 1,
        "column": 0,
        "cost": 2
      }
    ],
    "unmatched_columns": [],
    "total_cost": 3
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "assignment-hungarian-solve",
  "version": "1.0.0",
  "input": {
    "costs": [
      [
        4,
        1
      ],
      [
        2,
        3
      ]
    ],
    "unmatched_row_cost": 9,
    "unmatched_column_cost": 9
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/assignment-hungarian-solve/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"costs":[[4,1],[2,3]],"unmatched_row_cost":9,"unmatched_column_cost":9}'

The machine-readable contract is at /v1/tools/assignment-hungarian-solve/versions/1.0.0.

CLI

node cli.mjs run assignment-hungarian-solve 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

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