{
  "x402Version": 2,
  "id": 28629,
  "slug": "28629",
  "resource": "https://decision-solver.use.x402atlas.com/bin-pack",
  "description": "Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for placing items into bins, with feasibility evidence and an honest volume bound.",
  "type": "http",
  "serviceName": "Bounded Decision Solver",
  "resourceType": "Market Data",
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                "format": "uri",
                "maxLength": 512,
                "type": "string"
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                "description": "Bounded related Atlas routes",
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                "description": "Per-bin capacity",
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                "const": true,
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                "const": true,
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                "description": "Number of input items conserved by the packing",
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                "minimum": 1,
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            "description": "Produced bin count; it is not necessarily the unknown optimum",
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            "const": "bin-pack",
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            "description": "True only when produced bin count equals the valid volume lower bound; false makes no claim about the unknown optimum",
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            "maximum": 999,
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            "type": "integer"
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            "description": "Present only when optimal is true; omitted when optimal is false",
            "type": "string"
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            "additionalProperties": false,
            "description": "Deterministic best-fit-decreasing packing",
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                "description": "Number of produced bins",
                "maximum": 1000,
                "minimum": 0,
                "type": "integer"
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                "items": {
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                  "properties": {
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                      "maximum": 999,
                      "minimum": 0,
                      "type": "integer"
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                    "items": {
                      "description": "Items placed in this bin in deterministic placement order",
                      "items": {
                        "additionalProperties": false,
                        "description": "One conserved item placement",
                        "properties": {
                          "id": {
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                            "maxLength": 64,
                            "minLength": 1,
                            "pattern": "^[ -~]+$",
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                            "description": "Input item size",
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                      "minItems": 1,
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                      "maximum": 1000000000,
                      "minimum": 0,
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                      "description": "Capacity minus load",
                      "maximum": 1000000000,
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            "description": "Required honesty warning that the heuristic bound is not the actual optimality gap",
            "items": {
              "description": "Human-readable heuristic interpretation warning",
              "type": "string"
            },
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            "minItems": 1,
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          },
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                "size": 4
              }
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          "bodyType": "json",
          "method": "POST",
          "type": "http"
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              "algorithm": "best-fit-decreasing-v1",
              "capacity": 10,
              "capacity_feasible": true,
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              "volume_lower_bound": 3
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            "objective_value": 4,
            "operation": "bin-pack",
            "optimal": false,
            "optimality_gap_upper_bound": 1,
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              "bins": [
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                  "items": [
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                  "load": 8,
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                  "load": 5,
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            "warnings": [
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            ],
            "work_units": 10
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                    "maximum": 1000000000,
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                  "items": {
                    "description": "Unique-ID positive-size items; every size must be no greater than capacity",
                    "items": {
                      "additionalProperties": false,
                      "description": "One indivisible item to pack",
                      "properties": {
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                          "description": "Unique printable-ASCII item identifier",
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                          "pattern": "^[ -~]+$",
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                    "description": "Atlas documentation and related-route metadata added after deployment",
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                        "format": "uri",
                        "maxLength": 512,
                        "type": "string"
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                      "related": {
                        "description": "Bounded related Atlas routes",
                        "items": {
                          "additionalProperties": false,
                          "description": "One related Atlas route",
                          "properties": {
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                              "description": "Related bridge name",
                              "maxLength": 64,
                              "type": "string"
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                              "maxLength": 512,
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                              "description": "Short capability summary",
                              "maxLength": 256,
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                    "required": [
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                  "certificate": {
                    "additionalProperties": false,
                    "description": "Independently checkable feasibility, conservation, and volume-lower-bound evidence; not a general optimality certificate",
                    "properties": {
                      "algorithm": {
                        "const": "best-fit-decreasing-v1",
                        "description": "Heuristic algorithm used to produce the packing",
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                        "const": true,
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                      "item_count": {
                        "description": "Number of input items conserved by the packing",
                        "maximum": 1000,
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                        "description": "Sum of all input item sizes",
                        "maximum": 1000000000000,
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                      "volume_lower_bound": {
                        "description": "ceil(total_size/capacity), a valid lower bound on optimum bin count",
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                    "required": [
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                      "item_count",
                      "total_size",
                      "capacity",
                      "volume_lower_bound",
                      "item_conservation",
                      "capacity_feasible"
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                    "const": "minimum_bin_count",
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                    "description": "Produced bin count; it is not necessarily the unknown optimum",
                    "maximum": 1000,
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                  "operation": {
                    "const": "bin-pack",
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                    "description": "True only when produced bin count equals the valid volume lower bound; false makes no claim about the unknown optimum",
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                    "description": "Deterministic best-fit-decreasing packing",
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                        "description": "Produced bins in stable creation order",
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                              "description": "Stable zero-based bin index",
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                            "items": {
                              "description": "Items placed in this bin in deterministic placement order",
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                                "additionalProperties": false,
                                "description": "One conserved item placement",
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                              "maxItems": 1000,
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                              "maximum": 1000000000,
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                            "remaining": {
                              "description": "Capacity minus load",
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                    "required": [
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                    "type": "object"
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                  "warnings": {
                    "description": "Required honesty warning that the heuristic bound is not the actual optimality gap",
                    "items": {
                      "description": "Human-readable heuristic interpretation warning",
                      "type": "string"
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                    "maxItems": 1,
                    "minItems": 1,
                    "type": "array"
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                  "work_units": {
                    "description": "Candidate-bin feasibility checks performed by the heuristic",
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            "type": "object"
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        "required": [
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        "type": "object"
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      "tags": [
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        "operations-research",
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  "tags": [
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  "sourceHost": "decision-solver.use.x402atlas.com",
  "lastUpdated": "2026-10-06T04:27:33.297Z",
  "quality": {
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    "uniquePayers30d": 2,
    "lastCalledAt": "2026-10-06T04:27:33.164Z"
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  "metadata": {
    "serviceName": "Bounded Decision Solver",
    "extensions": {
      "bazaar": {
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                    "remaining": 5
                  }
                ]
              },
              "warnings": [
                "Best-fit decreasing is a heuristic; a nonzero reported bound is only an upper bound on the unknown optimality gap."
              ],
              "work_units": 10
            },
            "type": "json"
          }
        },
        "schema": {
          "$schema": "https://json-schema.org/draft/2020-12/schema",
          "properties": {
            "input": {
              "additionalProperties": false,
              "properties": {
                "body": {
                  "additionalProperties": false,
                  "properties": {
                    "capacity": {
                      "description": "Capacity of every produced bin",
                      "maximum": 1000000000,
                      "minimum": 1,
                      "type": "integer"
                    },
                    "items": {
                      "description": "Unique-ID positive-size items; every size must be no greater than capacity",
                      "items": {
                        "additionalProperties": false,
                        "description": "One indivisible item to pack",
                        "properties": {
                          "id": {
                            "description": "Unique printable-ASCII item identifier",
                            "maxLength": 64,
                            "minLength": 1,
                            "pattern": "^[ -~]+$",
                            "type": "string"
                          },
                          "size": {
                            "description": "Positive size not exceeding the request capacity",
                            "maximum": 1000000000,
                            "minimum": 1,
                            "type": "integer"
                          }
                        },
                        "required": [
                          "id",
                          "size"
                        ],
                        "type": "object"
                      },
                      "maxItems": 1000,
                      "minItems": 1,
                      "type": "array"
                    }
                  },
                  "required": [
                    "capacity",
                    "items"
                  ],
                  "type": "object"
                },
                "bodyType": {
                  "enum": [
                    "json",
                    "form-data",
                    "text"
                  ],
                  "type": "string"
                },
                "method": {
                  "enum": [
                    "POST"
                  ],
                  "type": "string"
                },
                "type": {
                  "const": "http",
                  "type": "string"
                }
              },
              "required": [
                "type",
                "method",
                "bodyType",
                "body"
              ],
              "type": "object"
            },
            "output": {
              "properties": {
                "example": {
                  "additionalProperties": false,
                  "properties": {
                    "_atlas": {
                      "additionalProperties": false,
                      "description": "Atlas documentation and related-route metadata added after deployment",
                      "properties": {
                        "docs": {
                          "description": "Documentation URL for this bridge",
                          "format": "uri",
                          "maxLength": 512,
                          "type": "string"
                        },
                        "related": {
                          "description": "Bounded related Atlas routes",
                          "items": {
                            "additionalProperties": false,
                            "description": "One related Atlas route",
                            "properties": {
                              "bridge": {
                                "description": "Related bridge name",
                                "maxLength": 64,
                                "type": "string"
                              },
                              "docs": {
                                "description": "Related bridge documentation URL",
                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
                              },
                              "summary": {
                                "description": "Short capability summary",
                                "maxLength": 256,
                                "type": "string"
                              },
                              "url": {
                                "description": "Related route URL",
                                "format": "uri",
                                "maxLength": 512,
                                "type": "string"
                              }
                            },
                            "required": [
                              "bridge",
                              "url",
                              "docs",
                              "summary"
                            ],
                            "type": "object"
                          },
                          "maxItems": 3,
                          "type": "array"
                        }
                      },
                      "required": [
                        "docs"
                      ],
                      "type": "object"
                    },
                    "algorithm_version": {
                      "const": "best-fit-decreasing-v1",
                      "description": "Pinned deterministic best-fit-decreasing heuristic contract",
                      "type": "string"
                    },
                    "certificate": {
                      "additionalProperties": false,
                      "description": "Independently checkable feasibility, conservation, and volume-lower-bound evidence; not a general optimality certificate",
                      "properties": {
                        "algorithm": {
                          "const": "best-fit-decreasing-v1",
                          "description": "Heuristic algorithm used to produce the packing",
                          "type": "string"
                        },
                        "capacity": {
                          "description": "Per-bin capacity",
                          "maximum": 1000000000,
                          "minimum": 1,
                          "type": "integer"
                        },
                        "capacity_feasible": {
                          "const": true,
                          "description": "True when every produced bin load is at most capacity",
                          "type": "boolean"
                        },
                        "item_conservation": {
                          "const": true,
                          "description": "True when every input item appears exactly once in the solution",
                          "type": "boolean"
                        },
                        "item_count": {
                          "description": "Number of input items conserved by the packing",
                          "maximum": 1000,
                          "minimum": 1,
                          "type": "integer"
                        },
                        "total_size": {
                          "description": "Sum of all input item sizes",
                          "maximum": 1000000000000,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "volume_lower_bound": {
                          "description": "ceil(total_size/capacity), a valid lower bound on optimum bin count",
                          "maximum": 1000,
                          "minimum": 1,
                          "type": "integer"
                        }
                      },
                      "required": [
                        "algorithm",
                        "item_count",
                        "total_size",
                        "capacity",
                        "volume_lower_bound",
                        "item_conservation",
                        "capacity_feasible"
                      ],
                      "type": "object"
                    },
                    "objective": {
                      "const": "minimum_bin_count",
                      "description": "The heuristic attempts to minimize produced bin count without exact search",
                      "type": "string"
                    },
                    "objective_value": {
                      "description": "Produced bin count; it is not necessarily the unknown optimum",
                      "maximum": 1000,
                      "minimum": 0,
                      "type": "integer"
                    },
                    "operation": {
                      "const": "bin-pack",
                      "description": "Stable route operation name",
                      "type": "string"
                    },
                    "optimal": {
                      "description": "True only when produced bin count equals the valid volume lower bound; false makes no claim about the unknown optimum",
                      "type": "boolean"
                    },
                    "optimality_gap_upper_bound": {
                      "description": "Produced bin count minus volume lower bound; an upper bound on the unknown optimality gap, never the actual gap",
                      "maximum": 999,
                      "minimum": 0,
                      "type": "integer"
                    },
                    "optimality_proof": {
                      "const": "matches-volume-lower-bound",
                      "description": "Present only when optimal is true; omitted when optimal is false",
                      "type": "string"
                    },
                    "solution": {
                      "additionalProperties": false,
                      "description": "Deterministic best-fit-decreasing packing",
                      "properties": {
                        "bin_count": {
                          "description": "Number of produced bins",
                          "maximum": 1000,
                          "minimum": 0,
                          "type": "integer"
                        },
                        "bins": {
                          "description": "Produced bins in stable creation order",
                          "items": {
                            "additionalProperties": false,
                            "description": "One produced bin",
                            "properties": {
                              "index": {
                                "description": "Stable zero-based bin index",
                                "maximum": 999,
                                "minimum": 0,
                                "type": "integer"
                              },
                              "items": {
                                "description": "Items placed in this bin in deterministic placement order",
                                "items": {
                                  "additionalProperties": false,
                                  "description": "One conserved item placement",
                                  "properties": {
                                    "id": {
                                      "description": "Input item identifier",
                                      "maxLength": 64,
                                      "minLength": 1,
                                      "pattern": "^[ -~]+$",
                                      "type": "string"
                                    },
                                    "original_index": {
                                      "description": "Zero-based input index",
                                      "maximum": 999,
                                      "minimum": 0,
                                      "type": "integer"
                                    },
                                    "size": {
                                      "description": "Input item size",
                                      "maximum": 1000000000,
                                      "minimum": 0,
                                      "type": "integer"
                                    }
                                  },
                                  "required": [
                                    "id",
                                    "original_index",
                                    "size"
                                  ],
                                  "type": "object"
                                },
                                "maxItems": 1000,
                                "minItems": 1,
                                "type": "array"
                              },
                              "load": {
                                "description": "Total item size in this bin",
                                "maximum": 1000000000,
                                "minimum": 0,
                                "type": "integer"
                              },
                              "remaining": {
                                "description": "Capacity minus load",
                                "maximum": 1000000000,
                                "minimum": 0,
                                "type": "integer"
                              }
                            },
                            "required": [
                              "index",
                              "load",
                              "remaining",
                              "items"
                            ],
                            "type": "object"
                          },
                          "maxItems": 1000,
                          "minItems": 1,
                          "type": "array"
                        }
                      },
                      "required": [
                        "bins",
                        "bin_count"
                      ],
                      "type": "object"
                    },
                    "warnings": {
                      "description": "Required honesty warning that the heuristic bound is not the actual optimality gap",
                      "items": {
                        "description": "Human-readable heuristic interpretation warning",
                        "type": "string"
                      },
                      "maxItems": 1,
                      "minItems": 1,
                      "type": "array"
                    },
                    "work_units": {
                      "description": "Candidate-bin feasibility checks performed by the heuristic",
                      "maximum": 1000000,
                      "minimum": 0,
                      "type": "integer"
                    }
                  },
                  "required": [
                    "operation",
                    "algorithm_version",
                    "objective",
                    "objective_value",
                    "optimal",
                    "optimality_gap_upper_bound",
                    "solution",
                    "work_units",
                    "certificate",
                    "warnings"
                  ],
                  "type": "object"
                },
                "type": {
                  "type": "string"
                }
              },
              "required": [
                "type"
              ],
              "type": "object"
            }
          },
          "required": [
            "input"
          ],
          "type": "object"
        },
        "tags": [
          "bin-packing-heuristic",
          "optimization",
          "operations-research",
          "bounded-computation",
          "deterministic"
        ]
      }
    }
  },
  "liveness": {
    "reliability": null
  },
  "verified": false,
  "featured": false,
  "provider": {
    "host": "decision-solver.use.x402atlas.com",
    "manifest_name": "decision-solver.use.x402atlas.com",
    "source": "cdp-mirror",
    "source_manifest_url": "https://api.cdp.coinbase.com/platform/v2/x402/discovery/resources",
    "submitted_at": "2026-10-14T01:15:01.050Z"
  },
  "exampleResponse": {
    "algorithm_version": "best-fit-decreasing-v1",
    "certificate": {
      "algorithm": "best-fit-decreasing-v1",
      "capacity": 10,
      "capacity_feasible": true,
      "item_conservation": true,
      "item_count": 5,
      "total_size": 30,
      "volume_lower_bound": 3
    },
    "objective": "minimum_bin_count",
    "objective_value": 4,
    "operation": "bin-pack",
    "optimal": false,
    "optimality_gap_upper_bound": 1,
    "solution": {
      "bin_count": 4,
      "bins": [
        {
          "index": 0,
          "items": [
            {
              "id": "a",
              "original_index": 0,
              "size": 8
            }
          ],
          "load": 8,
          "remaining": 2
        },
        {
          "index": 1,
          "items": [
            {
              "id": "b",
              "original_index": 1,
              "size": 7
            }
          ],
          "load": 7,
          "remaining": 3
        },
        {
          "index": 2,
          "items": [
            {
              "id": "c",
              "original_index": 2,
              "size": 6
            },
            {
              "id": "e",
              "original_index": 4,
              "size": 4
            }
          ],
          "load": 10,
          "remaining": 0
        },
        {
          "index": 3,
          "items": [
            {
              "id": "d",
              "original_index": 3,
              "size": 5
            }
          ],
          "load": 5,
          "remaining": 5
        }
      ]
    },
    "warnings": [
      "Best-fit decreasing is a heuristic; a nonzero reported bound is only an upper bound on the unknown optimality gap."
    ],
    "work_units": 10
  }
}