{"paper":{"title":"Time and Supply Fairness in Electricity Distribution using $k$-times bin packing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Every electricity division problem can be solved exactly by k-times bin packing with k depending only on the number of households.","cross_cats":["cs.MA"],"primary_cat":"cs.DS","authors_text":"Alex Ravsky, Dinesh Kumar Baghel, Erel Segal-Halevi","submitted_at":"2026-05-12T23:13:44Z","abstract_excerpt":"Given items of different sizes and a fixed bin capacity, the bin-packing problem is to pack these items into the minimum number of bins such that the sum of the item sizes in each bin does not exceed the capacity. We define a new variant, k-times bin-packing (kBP), in which the goal is to pack the items so that each item appears exactly k times in k different bins. We generalize existing approximation algorithms for bin-packing to solve kBP and analyze their performance ratios. The fair electricity division problem motivates the study of kBP. The goal is to allocate the available supply among "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that every electricity division problem can be solved by k-times bin-packing for some finite k, which depends only on the number of households.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That household electricity demands can be represented as fixed item sizes whose sums fit the bin-capacity model without distorting the egalitarian fairness criteria, and that the required k remains independent of the specific demand values.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"k-times bin-packing reduces fair electricity division to a finite-k packing problem, with generalized First-Fit algorithms outperforming heuristics on real demand data for egalitarian time allocation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every electricity division problem can be solved exactly by k-times bin packing with k depending only on the number of households.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0e1b41b26e068630304711593d44609293efa72f9a6dc54a20984a8b03d99f48"},"source":{"id":"2605.12812","kind":"arxiv","version":1},"verdict":{"id":"660324cd-6482-4611-b5d4-430693bcfcae","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:25:55.486856Z","strongest_claim":"We prove that every electricity division problem can be solved by k-times bin-packing for some finite k, which depends only on the number of households.","one_line_summary":"k-times bin-packing reduces fair electricity division to a finite-k packing problem, with generalized First-Fit algorithms outperforming heuristics on real demand data for egalitarian time allocation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That household electricity demands can be represented as fixed item sizes whose sums fit the bin-capacity model without distorting the egalitarian fairness criteria, and that the required k remains independent of the specific demand values.","pith_extraction_headline":"Every electricity division problem can be solved exactly by k-times bin packing with k depending only on the number of households."},"references":{"count":47,"sample":[{"doi":"","year":2017,"title":"IEEE intelligent systems 32(1), 24–31 (2017)","work_id":"12ac32e5-2fb1-4861-a1d7-0604554b3809","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-3-030-55187-2_32","year":2021,"title":"Advances in Intelligent Systems and Computing1251 AISC, 407–424 (2021).https://doi.org/ 10.1007/978-3-030-55187-2_32","work_id":"f37a6eab-0f83-46ef-bd0f-3655fbe179ed","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Competitive algorithms for server problems","work_id":"3d0c90fd-61ef-44af-8fee-6cbef7041958","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1017/cbo9780511598975","year":1996,"title":"Cambridge University Press (1996).https://doi.org/10.1017/CBO9780511598975","work_id":"12e24bec-49dc-4e9d-becd-288eaf7b3bcb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Pro- ceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020-May(Aamas), 204–212 (2020)","work_id":"10e549db-d2af-425b-b468-f05ae8e0439b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":47,"snapshot_sha256":"1c63c3990152c1fbd00318bf6e5fcf320af261c9144a3ced8cef98166e456315","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}