Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for placing it
Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for placing items into bins, with feasibility evidence and an honest volume bound.
5000 (raw units)
price
2
calls / 30d
1
unique payers
2026-09-15
updated
Provider
decision-solver.use.x402atlas.com · discovered, not yet claimed by its owner
Payment (x402 accepts[])
[
{
"scheme": "exact",
"network": "eip155:8453",
"payTo": "0x8C128f1Ee62Bb5e47867CfbAe2ad89be325Df1b2",
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"amount": "5000",
"maxTimeoutSeconds": 300
},
{
"scheme": "exact",
"network": "eip155:137",
"payTo": "0x8C128f1Ee62Bb5e47867CfbAe2ad89be325Df1b2",
"asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
"amount": "5000",
"maxTimeoutSeconds": 300
},
{
"scheme": "exact",
"network": "eip155:42161",
"payTo": "0x8C128f1Ee62Bb5e47867CfbAe2ad89be325Df1b2",
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"amount": "5000",
"maxTimeoutSeconds": 300
}
]Output schema
{
"bazaar": {
"category": "utilities",
"info": {
"input": {
"body": {
"capacity": 10,
"items": [
{
"id": "a",
"size": 8
},
{
"id": "b",
"size": 7
},
{
"id": "c",
"size": 6
},
{
"id": "d",
"size": 5
},
{
"id": "e",
"size": 4
}
]
},
"bodyType": "json",
"method": "POST",
"type": "http"
},
"output": {
"example": {
"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
},
"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"
]
}
}Use it
curl
curl "https://decision-solver.use.x402atlas.com/bin-pack" # -> 402 Payment Required, accepts[] lists how to pay # retry with a PAYMENT-SIGNATURE (or PAYMENT header) once paid
JavaScript
const res = await fetch("https://decision-solver.use.x402atlas.com/bin-pack");
if (res.status === 402) {
const { accepts } = await res.json();
// pay one of accepts[] via an x402 client, then retry with the payment header
}Python
import httpx
res = httpx.get("https://decision-solver.use.x402atlas.com/bin-pack")
if res.status_code == 402:
accepts = res.json()["accepts"]
# pay one of accepts[] via an x402 client, then retry with the payment headerMachine-readable
Everything on this page is also available as clean JSON at /resources/3464.json, and this resource appears in /discovery/resources and /discovery/search.