{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:56:49Z","timestamp":1773802609745,"version":"3.50.1"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"20","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>We study the problem of fairly and efficiently allocating indivisible goods among agents with additive valuations. We focus on envy-freeness up to any good (EFX) \u2014 an important fairness notion in fair division of indivisible goods. A central open question in this field is whether EFX allocations always exist for any number of agents. While recent results have established EFX existence for settings with at most three distinct valuations and for two types of goods, the general case remains unresolved.\n\nIn this paper, we extend the existent knowledge by proving that EFX allocations satisfying Pareto optimality (PO) always exist and can be computed in quasiliniear time when there are two types of goods, given that the valuations are positive. Our findings demonstrate a fairly simple and efficient algorithm constructing an EFX+PO allocation.<\/jats:p>","DOI":"10.1609\/aaai.v40i20.38723","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:50:02Z","timestamp":1773795002000},"page":"16795-16802","source":"Crossref","is-referenced-by-count":0,"title":["EFX and PO Allocation Exists for Two Types of Goods"],"prefix":"10.1609","volume":"40","author":[{"given":"Vladimir","family":"Davidiuk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuriy","family":"Dementiev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Artur","family":"Ignatiev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danil","family":"Sagunov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9382","published-online":{"date-parts":[[2026,3,14]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38723\/42685","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38723\/42685","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:50:03Z","timestamp":1773795003000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/38723"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,14]]},"references-count":0,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2026,3,17]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v40i20.38723","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3,14]]}}}