{"title":"层次和一维周期性指定问题的复杂性I:硬度结果","authors":"M. Marathe, H. Hunt, R. Stearns, V. Radhakrishnan","doi":"10.1090/dimacs/035/05","DOIUrl":null,"url":null,"abstract":"We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances.","PeriodicalId":434373,"journal":{"name":"Satisfiability Problem: Theory and Applications","volume":"447 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"Complexity of hierarchically and 1-dimensional periodically specified problems I: Hardness results\",\"authors\":\"M. Marathe, H. Hunt, R. Stearns, V. Radhakrishnan\",\"doi\":\"10.1090/dimacs/035/05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances.\",\"PeriodicalId\":434373,\"journal\":{\"name\":\"Satisfiability Problem: Theory and Applications\",\"volume\":\"447 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Satisfiability Problem: Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/dimacs/035/05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Satisfiability Problem: Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/dimacs/035/05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
摘要
我们研究了当实例使用下列规范之一指定时各种组合和可满足性问题的复杂性:(1) Wanke和Ford等人的一维有限周期窄规范;(2)Gale带显边界条件的一维有限周期窄规范;(3)Orlin等人的二维无限一维窄周期规范;(4)Lengauer等人的分层规范。首先,我们证明了存在一个多项式时间算法,给定图的1-FPN-或1-FPN(BC)规范(或C N F公式),构造同构图(或公式)的水平限制l规范。这个定理与这里证明的硬度结果一起,为过去由Lengauer和Wagner或Orlin证明的许多硬度结果提供了替代的和统一的证明。其次,研究了Schaefer广义CNF可满足问题的复杂性。假设P {ne} PSPACE,当实例指定为(1)、(2)、(3)或(4)时,我们完全描述了这些问题的多项式时间可解性。作为前两类结果的应用,我们获得了许多新的PSPACE-硬度和多项式时间算法,用于指定为(1)、(2)、(3)或(4)的问题。我们的许多结果也适用于O(log N)带宽受限的平面实例。
Complexity of hierarchically and 1-dimensional periodically specified problems I: Hardness results
We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances.