{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T16:54:14Z","timestamp":1692982454907},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[1993,3]]},"abstract":"<jats:p> In this paper, we study a simple combinatorial property of maximization problems and we establish some interesting connections between such a property and the class [Formula: see text] defined by Papadimitriou and Yannakakis. <\/jats:p><jats:p> In particular, we first prove that any maximization problem in [Formula: see text] has guaranteed average measure, that is, the average measure of the feasible solutions is no less than a constant fraction of the optimum measure (this intuitively justifies the fact that any problem in [Formula: see text] is approximable). <\/jats:p><jats:p> Successively, we prove that there exist maximization problems that do not belong to [Formula: see text] but still have guaranteed average measure. Hence, such a property does not characterize the class [Formula: see text]. <\/jats:p><jats:p> Finally, we show that there are several maximization problems which do not have guaranteed average measure and, hence, do not belong to [Formula: see text]. In this context, the notion of a problem with guaranteed average measure seems to be a powerful and very easy-to-use tool that allows us to prove that optimization problems are not in [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0129054193000031","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"15-30","source":"Crossref","is-referenced-by-count":5,"title":["AVERAGE MEASURE, DESCRIPTIVE COMPLEXITY AND APPROXIMATION OF MAXIMIZATION PROBLEMS"],"prefix":"10.1142","volume":"04","author":[{"given":"PIERLUIGI","family":"CRESCENZI","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze dell\u2019Informazione, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Via Salaria 113, I\u201300198 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RICCARDO","family":"SILVESTRI","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze dell\u2019Informazione, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Via Salaria 113, I\u201300198 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054193000031","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:55:31Z","timestamp":1565139331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054193000031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,3]]}},"alternative-id":["10.1142\/S0129054193000031"],"URL":"https:\/\/doi.org\/10.1142\/s0129054193000031","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}