{"slug":"decision-solver-use-x402atlas-com-bin-pack-5baa0a","title":"Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for ","host":"decision-solver.use.x402atlas.com","method":"POST","resource":"https://decision-solver.use.x402atlas.com/bin-pack","category":"other","description":"Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for placing items into bins, with feasibility evidence and an honest volume bound.","price_listed":0.005,"price_asked":0.005,"state":"answering","state_label":"Answering","checks_7d":1,"answered_7d":1,"latency_ms_median":656,"reported_calls_30d":2,"reported_payers_30d":1,"networks":["eip155:137","eip155:42161","eip155:8453"],"badge":"unverified","paid_checks_7d":0,"paid_ok_7d":0,"example_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_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"},"history":[{"day":"2026-09-24","reachable":true,"status":402,"valid_402":true,"asked_usdc":0.005,"price_match":true,"latency_ms":656,"error":null}],"description_full":"Bin-packing heuristic — deterministic best-fit-decreasing capacity planning for placing items into bins, with feasibility evidence and an honest volume bound.","last_updated":"2026-09-15T06:32:25.965Z","schemes":["exact"]}