It is shown that the following minimum cover problems are NP-hard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the polygons are required to be in general position.<>
{"title":"Covering polygons is hard","authors":"J. Culberson, R. Reckhow","doi":"10.1109/SFCS.1988.21976","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21976","url":null,"abstract":"It is shown that the following minimum cover problems are NP-hard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the polygons are required to be in general position.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115480282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A fast randomized algorithm is given for finding a partition of the plane induced by a given set of linear segments. The algorithm is ideally suited for a practical use because it is extremely simple and robust, as well as optimal; its expected running time is O(m+n log n) where n is the number of input segments and m is the number of points of intersection. The storage requirement is O(m+n). Though the algorithm itself is simple, the global evolution of the partition is complex, which makes the analysis of the algorithm theoretically interesting in its own right.<>
{"title":"A fast planar partition algorithm. I","authors":"K. Mulmuley","doi":"10.1109/SFCS.1988.21974","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21974","url":null,"abstract":"A fast randomized algorithm is given for finding a partition of the plane induced by a given set of linear segments. The algorithm is ideally suited for a practical use because it is extremely simple and robust, as well as optimal; its expected running time is O(m+n log n) where n is the number of input segments and m is the number of points of intersection. The storage requirement is O(m+n). Though the algorithm itself is simple, the global evolution of the partition is complex, which makes the analysis of the algorithm theoretically interesting in its own right.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125858467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A generalization of the maximum-flow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e) lambda (e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. Conservation of flow is required at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. The authors present polynomial-time combinatorial algorithms for this problem. The algorithms are simple and intuitive.<>
{"title":"Combinatorial algorithms for the generalized circulation problem","authors":"A. Goldberg, Serge A. Plotkin, É. Tardos","doi":"10.1109/SFCS.1988.21959","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21959","url":null,"abstract":"A generalization of the maximum-flow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e) lambda (e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. Conservation of flow is required at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. The authors present polynomial-time combinatorial algorithms for this problem. The algorithms are simple and intuitive.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"334 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127574669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of learning a concept from examples in a distribution-free model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite Vapnik-Chervonenkis (VC) dimension. An important variation on the problem of learning from examples, called approximating from examples, is also discussed. The problem of computing the VC dimension of a finite concept set defined on a finite domain is considered.<>
{"title":"Results on learnability and the Vapnik-Chervonenkis dimension","authors":"N. Linial, Y. Mansour, R. Rivest","doi":"10.1109/SFCS.1988.21930","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21930","url":null,"abstract":"The problem of learning a concept from examples in a distribution-free model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite Vapnik-Chervonenkis (VC) dimension. An important variation on the problem of learning from examples, called approximating from examples, is also discussed. The problem of computing the VC dimension of a finite concept set defined on a finite domain is considered.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130503299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of determining the cost of random-access memory (RAM) is addressed by studying the simulation of random addressing by a machine which lacks it, called a pointer machine. The model allows the use of a data type of choice. A RAM program of time t and space s can be simulated in O(t log s) time using a tree. However, this is not an obvious lower bound since a high-level data type can allow the data to be encoded in a more economical way. The major contribution is the formalization of incompressibility for general data types. The definition extends a similar property of strings that underlies the theory of Kolmogorov complexity. The main theorem states that for all incompressible data types an Omega (t log s) lower bound holds. Incompressibility is proved for the real numbers with a set of primitives which includes all functions which are continuously differentiable except on a countable closed set.<>
{"title":"On pointers versus addresses","authors":"Amir M. Ben-Amram, Z. Galil","doi":"10.1145/146637.146666","DOIUrl":"https://doi.org/10.1145/146637.146666","url":null,"abstract":"The problem of determining the cost of random-access memory (RAM) is addressed by studying the simulation of random addressing by a machine which lacks it, called a pointer machine. The model allows the use of a data type of choice. A RAM program of time t and space s can be simulated in O(t log s) time using a tree. However, this is not an obvious lower bound since a high-level data type can allow the data to be encoded in a more economical way. The major contribution is the formalization of incompressibility for general data types. The definition extends a similar property of strings that underlies the theory of Kolmogorov complexity. The main theorem states that for all incompressible data types an Omega (t log s) lower bound holds. Incompressibility is proved for the real numbers with a set of primitives which includes all functions which are continuously differentiable except on a countable closed set.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132258982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The question of how to learn rules, when those rules make probabilistic statements about the future, is considered. Issues are discussed that arise when attempting to determine what a good prediction function is, when those prediction functions make probabilistic assumptions. Learning has at least two purposes: to enable the learner to make predictions in the future and to satisfy intellectual curiosity as to the underlying cause of a process. Two results related to these distinct goals are given. In both cases, the inputs are a countable collection of functions which make probabilistic statements about a sequence of events. One of the results shows how to find one of the functions, which generated the sequence, the other result allows to do as well in terms of predicting events as the best of the collection. In both cases the results are obtained by evaluating a function based on a tradeoff between its simplicity and the accuracy of its predictions.<>
{"title":"Learning probabilistic prediction functions","authors":"A. D. Santis, G. Markowsky, M. Wegman","doi":"10.1109/SFCS.1988.21929","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21929","url":null,"abstract":"The question of how to learn rules, when those rules make probabilistic statements about the future, is considered. Issues are discussed that arise when attempting to determine what a good prediction function is, when those prediction functions make probabilistic assumptions. Learning has at least two purposes: to enable the learner to make predictions in the future and to satisfy intellectual curiosity as to the underlying cause of a process. Two results related to these distinct goals are given. In both cases, the inputs are a countable collection of functions which make probabilistic statements about a sequence of events. One of the results shows how to find one of the functions, which generated the sequence, the other result allows to do as well in terms of predicting events as the best of the collection. In both cases the results are obtained by evaluating a function based on a tradeoff between its simplicity and the accuracy of its predictions.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121901036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The storage allocation for three stacks has been traditionally accomplished by using pointers to store the stacks as linked lists or by relocating the stacks within memory when collisions take place. The former approach requires additional space to store the pointers, and the latter approach requires additional time. The authors explore the extent to which some additional space or time is required to maintain three stacks. They provide a formal setting for this topic and establish upper and lower complexity bounds on various aspects.<>
{"title":"Three stacks","authors":"M. Fredman, D. Goldsmith","doi":"10.1109/SFCS.1988.21967","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21967","url":null,"abstract":"The storage allocation for three stacks has been traditionally accomplished by using pointers to store the stacks as linked lists or by relocating the stacks within memory when collisions take place. The former approach requires additional space to store the pointers, and the latter approach requires additional time. The authors explore the extent to which some additional space or time is required to maintain three stacks. They provide a formal setting for this topic and establish upper and lower complexity bounds on various aspects.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116779520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A lower bound for matrix multiplication","authors":"N. Bshouty","doi":"10.1109/SFCS.1988.21922","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21922","url":null,"abstract":"It is proved that computing the product of two n*n matrices over the binary field requires at least 2.5n/sup 2/-O(n/sup 2/) multiplications.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125347768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Much of what is known about the model theory and proof theory of the lambda -calculus is sensible in nature, i.e. only head normal forms are semantically meaningful. However, most functional languages are lazy, i.e. programs are evaluated in normal order to weak head normal forms. The author develops a theory of lazy or strongly sensible lambda -calculus that corresponds to practice. A general method for constructing fully abstract models for a class of lazy languages is illustrated. A formal system called lambda beta C ( lambda beta -calculus with convergence testing C) is introduced, and its properties are investigated.<>
关于λ演算的模型理论和证明理论的许多已知内容在本质上是合理的，即只有头部范式在语义上有意义。然而，大多数函数式语言都是懒惰的，即程序按照正常顺序进行评估，而不是按照正常形式进行评估。作者提出了一种符合实际的懒或强敏感λ演算理论。给出了构造一类惰性语言的全抽象模型的一般方法。引入了一种称为λ β C (λ β -带收敛性检验C的微积分)的形式系统，并研究了它的性质。
{"title":"Fully abstract models of the lazy lambda calculus","authors":"C. Ong","doi":"10.1109/SFCS.1988.21953","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21953","url":null,"abstract":"Much of what is known about the model theory and proof theory of the lambda -calculus is sensible in nature, i.e. only head normal forms are semantically meaningful. However, most functional languages are lazy, i.e. programs are evaluated in normal order to weak head normal forms. The author develops a theory of lazy or strongly sensible lambda -calculus that corresponds to practice. A general method for constructing fully abstract models for a class of lazy languages is illustrated. A formal system called lambda beta C ( lambda beta -calculus with convergence testing C) is introduced, and its properties are investigated.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116533440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martin Dietzfelbinger, Anna R. Karlin, K. Mehlhorn, F. Heide, H. Rohnert, R. Tarjan
A randomized algorithm is given for the dictionary problem with O(1) worst-case time for lookup and O(1) amortized expected time for insertion and deletion. An Omega (log n) lower bound is proved for the amortized worst-case time complexity of any deterministic algorithm in a class of algorithms encompassing realistic hashing-based schemes. If the worst-case lookup time is restricted to k, then the lower bound for insertion becomes Omega (kn/sup 1/k/).<>
{"title":"Dynamic perfect hashing: upper and lower bounds","authors":"Martin Dietzfelbinger, Anna R. Karlin, K. Mehlhorn, F. Heide, H. Rohnert, R. Tarjan","doi":"10.1109/SFCS.1988.21968","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21968","url":null,"abstract":"A randomized algorithm is given for the dictionary problem with O(1) worst-case time for lookup and O(1) amortized expected time for insertion and deletion. An Omega (log n) lower bound is proved for the amortized worst-case time complexity of any deterministic algorithm in a class of algorithms encompassing realistic hashing-based schemes. If the worst-case lookup time is restricted to k, then the lower bound for insertion becomes Omega (kn/sup 1/k/).<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126529527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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