{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T03:05:13Z","timestamp":1649127913540},"reference-count":2,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> Given a seller with m items, a sequence of users {u<jats:sub>1<\/jats:sub>, u<jats:sub>2<\/jats:sub>, \u2026} come one by one, the seller must set the unit price and assign some items to each user on his\/her arrival. Items can be sold fractionally. Each u<jats:sub>i<\/jats:sub> has his\/her value function v<jats:sub>i<\/jats:sub>(\u22c5) such that v<jats:sub>i<\/jats:sub>(x) is the highest unit price u<jats:sub>i<\/jats:sub> is willing to pay for x items. The objective is to maximize the revenue by setting the price and number of items for each user. In this paper, we have the following contributions: if the highest value h among all v<jats:sub>i<\/jats:sub>(x) is known in advance, we first show the lower bound of the competitive ratio is \u230a log h\u230b\/2, then give an online algorithm with competitive ratio 4\u230a log h\u230b + 6; if h is not known in advance, we give an online algorithm with competitive ratio 2\u22c5h<jats:sup> log <jats:sup>-1\/2<\/jats:sup> h<\/jats:sup> + 8\u22c5h<jats:sup>3 log <jats:sup>-1\/2<\/jats:sup> h<\/jats:sup>. <\/jats:p>","DOI":"10.1142\/s1793830912500152","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T10:55:53Z","timestamp":1340103353000},"page":"1250015","source":"Crossref","is-referenced-by-count":3,"title":["COMPETITIVE ALGORITHMS FOR ONLINE PRICING"],"prefix":"10.1142","volume":"04","author":[{"given":"YONG","family":"ZHANG","sequence":"first","affiliation":[{"name":"Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China"},{"name":"Department of Computer Science, The University of Hong Kong, Hong Kong"}]},{"given":"YUXIN","family":"WANG","sequence":"additional","affiliation":[{"name":"Computer Science and Technology School, Dalian University of Technology, China"}]},{"given":"FRANCIS Y. L.","family":"CHIN","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Hong Kong"}]},{"given":"HING-FUNG","family":"TING","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Hong Kong"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2007.v003a009"},{"key":"rf4","volume":"6","author":"Bansal N.","journal-title":"ACM Trans. Algorithms"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500152","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:42:05Z","timestamp":1565116925000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":2,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S1793830912500152"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500152","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}