{"title":"加权NP优化问题:逻辑可定义性和近似性质","authors":"Marius Zimand","doi":"10.1109/SCT.1995.514724","DOIUrl":null,"url":null,"abstract":"It is shown that all NP-optimization problems can be characterized by /spl Pi//sub 2/ first-order formulae and that /spl Pi//sub 1/ formulae are not sufficient for this goal. This generalizes the result of Kolaitis and Thakur (1990). The approximation properties of the weighted versions of MAX NP, MAX SNP, MAX SNP(/spl pi/), MIN F/sup +//spl Pi//sub 1/ and MIN F/sup +//spl Pi//sub 2/(1) are analyzed and dramatic changes are observed when negative weights are allowed.","PeriodicalId":318382,"journal":{"name":"Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Weighted NP optimization problems: logical definability and approximation properties\",\"authors\":\"Marius Zimand\",\"doi\":\"10.1109/SCT.1995.514724\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that all NP-optimization problems can be characterized by /spl Pi//sub 2/ first-order formulae and that /spl Pi//sub 1/ formulae are not sufficient for this goal. This generalizes the result of Kolaitis and Thakur (1990). The approximation properties of the weighted versions of MAX NP, MAX SNP, MAX SNP(/spl pi/), MIN F/sup +//spl Pi//sub 1/ and MIN F/sup +//spl Pi//sub 2/(1) are analyzed and dramatic changes are observed when negative weights are allowed.\",\"PeriodicalId\":318382,\"journal\":{\"name\":\"Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SCT.1995.514724\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1995.514724","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Weighted NP optimization problems: logical definability and approximation properties
It is shown that all NP-optimization problems can be characterized by /spl Pi//sub 2/ first-order formulae and that /spl Pi//sub 1/ formulae are not sufficient for this goal. This generalizes the result of Kolaitis and Thakur (1990). The approximation properties of the weighted versions of MAX NP, MAX SNP, MAX SNP(/spl pi/), MIN F/sup +//spl Pi//sub 1/ and MIN F/sup +//spl Pi//sub 2/(1) are analyzed and dramatic changes are observed when negative weights are allowed.
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