Random Minimum-Cost Flow Instance Generator

Description

Generate a capacitated directed network containing a spanning source-to-sink path, with a feasible fixed-amount flow and nonnegative unit costs witness; reverse arcs are allowed, with no cost-minimality claim.

An optimization instance defines choices, constraints, and an objective. A feasible witness demonstrates that its stated constraints can be met; it establishes optimality only when the tool actually computes and verifies an optimum.

When to use this tool

Use this generator to create reproducible min cost flow instance cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply nodeCount, arcCount, minimumCapacity, maximumCapacity, requiredFlow, minimumCost, maximumCost in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read nodes, source, sink, arcs, witnessPath, arcFlows, flowValue, totalCost. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Construct directed arcs containing a source-to-sink chain, draw integer capacities and unit costs, and send requiredFlow along that chain with zero flow on extra arcs. Return aligned arc flows and an exact safe-integer total cost.^[1]

Input field	Meaning and units	Accepted input
nodeCount	Node Count	Required. Safe integer; minimum 2; maximum 32.
arcCount	Arc Count	Required. Safe integer; minimum 1; maximum 992.
minimumCapacity	Minimum Capacity	Required. Safe integer; minimum 1; maximum 9007199254740991.
maximumCapacity	Maximum Capacity	Required. Safe integer; minimum 1; maximum 9007199254740991.
requiredFlow	Required Flow	Required. Safe integer; minimum 1; maximum 9007199254740991.
minimumCost	Minimum Cost	Required. Safe integer; minimum 0; maximum 9007199254740991.
maximumCost	Maximum Cost	Required. Safe integer; minimum 0; maximum 9007199254740991.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
nodes	Nodes	Required. Array of Safe integer; minimum 0; maximum 31.; minimum items 2; maximum items 32.
source	Source	Required. Safe integer; minimum 0; maximum 31.
sink	Sink	Required. Safe integer; minimum 0; maximum 31.
arcs	Arcs	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 992.
arcs[].from	From	Required. Safe integer; minimum 0; maximum 31.
arcs[].to	To	Required. Safe integer; minimum 0; maximum 31.
arcs[].capacity	Capacity	Required. Safe integer; minimum 1; maximum 9007199254740991.
arcs[].unitCost	Unit Cost	Required. Safe integer; minimum 0; maximum 9007199254740991.
witnessPath	Witness Path	Required. Array of Safe integer; minimum 0; maximum 31.; minimum items 2; maximum items 32.
arcFlows	Arc Flows	Required. Array of Safe integer; minimum 0; maximum 9007199254740991.; minimum items 1; maximum items 992.
flowValue	Flow Value	Required. Safe integer; minimum 1; maximum 9007199254740991.
totalCost	Total Cost	Required. Safe integer; minimum 0; maximum 9007199254740991.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "nodeCount": 4,
    "arcCount": 6,
    "minimumCapacity": 2,
    "maximumCapacity": 9,
    "requiredFlow": 2,
    "minimumCost": 0,
    "maximumCost": 5,
    "seed": 42
  },
  "output": {
    "nodes": [
      0,
      1,
      2,
      3
    ],
    "source": 0,
    "sink": 3,
    "arcs": [
      {
        "from": 0,
        "to": 1,
        "capacity": 5,
        "unitCost": 1
      },
      {
        "from": 1,
        "to": 2,
        "capacity": 9,
        "unitCost": 4
      },
      {
        "from": 2,
        "to": 3,
        "capacity": 4,
        "unitCost": 1
      },
      {
        "from": 0,
        "to": 2,
        "capacity": 6,
        "unitCost": 4
      },
      {
        "from": 3,
        "to": 1,
        "capacity": 6,
        "unitCost": 0
      },
      {
        "from": 1,
        "to": 3,
        "capacity": 5,
        "unitCost": 5
      }
    ],
    "witnessPath": [
      0,
      1,
      2,
      3
    ],
    "arcFlows": [
      2,
      2,
      2,
      0,
      0,
      0
    ],
    "flowValue": 2,
    "totalCost": 12,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Every possible chain capacity must support requiredFlow. The witness is feasible but not a minimum-cost flow; added arcs can offer cheaper alternatives and reverse directed pairs are allowed.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Minimum-Cost Flow Instance Generator — tool.io

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