DAG critical (longest) path API

Finds the longest-weighted path through a DAG of weighted nodes and returns earliest/latest start, finish and slack per node so zero-slack tasks are flagged as critical. Answers 'What is the longest path through my task graph?', 'Which steps have no schedule slack?'.

Price$0.03per request

MethodPOST

Route/v1/workflow/critical-path-graph

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

critical-pathlongest-pathdagslackgraphschedulecpmworkflow

API URLhttps://x402.hexl.dev/v1/workflow/critical-path-graph

Integration docs

Example request

{
  "nodes": [
    {
      "id": "a",
      "duration": 3
    },
    {
      "id": "b",
      "duration": 2
    },
    {
      "id": "c",
      "duration": 4
    }
  ],
  "edges": [
    [
      "a",
      "b"
    ],
    [
      "a",
      "c"
    ],
    [
      "b",
      "c"
    ]
  ]
}

Example response

{
  "criticalPath": [
    "a",
    "b",
    "c"
  ],
  "length": 9,
  "nodes": [
    {
      "id": "a",
      "es": 0,
      "ef": 3,
      "ls": 0,
      "lf": 3,
      "slack": 0
    },
    {
      "id": "b",
      "es": 3,
      "ef": 5,
      "ls": 3,
      "lf": 5,
      "slack": 0
    },
    {
      "id": "c",
      "es": 5,
      "ef": 9,
      "ls": 5,
      "lf": 9,
      "slack": 0
    }
  ],
  "interpretation": "Critical path a -> b -> c has length 9; zero-slack tasks are critical."
}

Input schema

{
  "type": "object",
  "required": [
    "nodes",
    "edges"
  ],
  "properties": {
    "nodes": {
      "type": "array",
      "examples": [
        [
          {
            "id": "a",
            "duration": 3
          },
          {
            "id": "b",
            "duration": 2
          },
          {
            "id": "c",
            "duration": 4
          }
        ]
      ]
    },
    "edges": {
      "type": "array",
      "examples": [
        [
          [
            "a",
            "b"
          ],
          [
            "a",
            "c"
          ],
          [
            "b",
            "c"
          ]
        ]
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}