Schedule critical path

schedule-critical-path · version 1.0.0 · Graphs & scheduling · free, no key needed

Compute CPM zero-slack critical nodes and tight edges on a DAG, plus one representative critical path.

Use when you need to: schedule critical path · cpm zero-slack critical path · critical nodes edges and representative path.

Supported

• schedule critical path
• cpm zero-slack critical path
• critical nodes edges and representative path

Not supported

• multiple enumerated critical paths
• probabilistic PERT
• crashing
• calendar dates and working hours

Behavior

• Input is a directed simple graph plus durations whose own keys are exactly the node ids, each a canonical non-negative integer string of at most 18 digits.
• Edge from→to is finish-to-start with lag 0: to cannot start before from finishes.
• The graph must be a DAG under Kahn order (smallest remaining indegree-0 declared index); a cycle including a self-loop throws invalid_input with a message containing cycle.
• ES[v] is 0 if v has no predecessors, else the maximum EF of its predecessors. EF[v] is ES[v] plus duration[v]. Times that exceed 18 digits throw.
• makespan is the maximum EF, or 0 when there are no nodes.
• Latest times walk the Kahn sequence backwards: LF[v] is makespan if v has no successors, else the minimum LS of its successors. LS[v] is LF[v] minus duration[v].
• Slack is LS minus ES (equal to LF minus EF). A node is critical iff its slack is 0.
• critical_nodes lists slack-0 ids in declared nodes order.
• critical_edges lists original edges in original edge order whose both ends are critical and EF[from] equals ES[to].
• The representative path is empty on the empty graph. Otherwise it starts at the smallest-index critical node with no incoming critical tight edge, then repeatedly appends the smallest-index successor reached by a critical tight edge.

Input

• nodes (array of string, required): max items 2000; each min length 1; each max length 256
• edges (array of object, required): max items 10000
• durations (object, required)

Output

• makespan (string, required): max length 18; pattern ^(0|[1-9][0-9]*)$
• critical_nodes (array of string, required): max items 2000; each min length 1; each max length 256
• critical_edges (array of object, required): max items 10000
• path (array of string, required): max items 2000; each min length 1; each max length 256

Limits

• max nodes: 2000
• max edges: 10000
• max node id bytes: 256
• max duration digits: 18

Example

Request input:

{
  "nodes": [
    "spec",
    "api",
    "ui",
    "integ",
    "ship"
  ],
  "edges": [
    {
      "from": "spec",
      "to": "api"
    },
    {
      "from": "spec",
      "to": "ui"
    },
    {
      "from": "api",
      "to": "integ"
    },
    {
      "from": "ui",
      "to": "integ"
    },
    {
      "from": "integ",
      "to": "ship"
    }
  ],
  "durations": {
    "spec": "2",
    "api": "5",
    "ui": "3",
    "integ": "4",
    "ship": "1"
  }
}

Response:

{
  "result": {
    "makespan": "12",
    "critical_nodes": [
      "spec",
      "api",
      "integ",
      "ship"
    ],
    "critical_edges": [
      {
        "from": "spec",
        "to": "api"
      },
      {
        "from": "api",
        "to": "integ"
      },
      {
        "from": "integ",
        "to": "ship"
      }
    ],
    "path": [
      "spec",
      "api",
      "integ",
      "ship"
    ]
  }
}

How to call it

MCP

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

{
  "id": "schedule-critical-path",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "spec",
      "api",
      "ui",
      "integ",
      "ship"
    ],
    "edges": [
      {
        "from": "spec",
        "to": "api"
      },
      {
        "from": "spec",
        "to": "ui"
      },
      {
        "from": "api",
        "to": "integ"
      },
      {
        "from": "ui",
        "to": "integ"
      },
      {
        "from": "integ",
        "to": "ship"
      }
    ],
    "durations": {
      "spec": "2",
      "api": "5",
      "ui": "3",
      "integ": "4",
      "ship": "1"
    }
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/schedule-critical-path/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["spec","api","ui","integ","ship"],"edges":[{"from":"spec","to":"api"},{"from":"spec","to":"ui"},{"from":"api","to":"integ"},{"from":"ui","to":"integ"},{"from":"integ","to":"ship"}],"durations":{"spec":"2","api":"5","ui":"3","integ":"4","ship":"1"}}'

The machine-readable contract is at /v1/tools/schedule-critical-path/versions/1.0.0.

CLI

node cli.mjs run schedule-critical-path 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Graph shortest unweighted path: Find a shortest directed path by fewest edges from source to target.
• Schedule earliest finish: Compute CPM earliest start and earliest finish times for a DAG with node durations, plus the project makespan.
• Graph validate: Inspect a well-formed directed simple graph and report counts, isolated nodes, and maximum degrees.
• Schedule ready nodes: List DAG nodes that can start because they are not completed and every predecessor is completed.
• Graph ancestors: List every ancestor of given targets, including the targets, in reverse-graph BFS discovery order.
• Graph DAG longest path: Return a longest node-weighted path in a DAG, where path weight is the sum of node durations.