Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185391
Nils Klarlund
A new approach to complementing omega -automata, which are finite-state automata defining languages of infinite words, is given. Instead of using usual combinatorial or algebraic properties of transition relations, it is shown that a graph-theoretic approach based on the notion of progress measures is a potent tool for complementing omega -automata. Progress measures are applied to the classical problem of complementing Buchi automata, and a simple method is obtained. The technique applies to Streett automata, for which an optimal complementation method is also obtained. As a consequence, it is seen that the powerful temporal logic ETLs is much more tractable than previously thought.<>
{"title":"Progress measures for complementation omega -automata with applications to temporal logic","authors":"Nils Klarlund","doi":"10.1109/SFCS.1991.185391","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185391","url":null,"abstract":"A new approach to complementing omega -automata, which are finite-state automata defining languages of infinite words, is given. Instead of using usual combinatorial or algebraic properties of transition relations, it is shown that a graph-theoretic approach based on the notion of progress measures is a potent tool for complementing omega -automata. Progress measures are applied to the classical problem of complementing Buchi automata, and a simple method is obtained. The technique applies to Streett automata, for which an optimal complementation method is also obtained. As a consequence, it is seen that the powerful temporal logic ETLs is much more tractable than previously thought.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134167351","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185444
P. Shor
An O(n log n)-time online algorithm is given for packing items i.i.d. uniform on (0, 1) into bins of size 1 with expected wasted space Theta (n/sup 1/2/ log /sup 1/2/n). This matches the lowest bound that no online algorithm can achieve O(n/sup 1/2/ log /sup 1/2/ n) wasted space. It is done by analyzing another algorithm which involves putting balls into buckets online. The analysis of this second algorithm also gives bound on the stochastic rightward matching problem, which arises in analyzing not only the above online bin packing problem, but also a 2-D problem of packing rectangles into a half-infinite strip. The bounds on rightward matching thus give good bounds for the 2-D strip packing problem.<>
{"title":"How to pack better than best fit: tight bounds for average-case online bin packing","authors":"P. Shor","doi":"10.1109/SFCS.1991.185444","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185444","url":null,"abstract":"An O(n log n)-time online algorithm is given for packing items i.i.d. uniform on (0, 1) into bins of size 1 with expected wasted space Theta (n/sup 1/2/ log /sup 1/2/n). This matches the lowest bound that no online algorithm can achieve O(n/sup 1/2/ log /sup 1/2/ n) wasted space. It is done by analyzing another algorithm which involves putting balls into buckets online. The analysis of this second algorithm also gives bound on the stochastic rightward matching problem, which arises in analyzing not only the above online bin packing problem, but also a 2-D problem of packing rectangles into a half-infinite strip. The bounds on rightward matching thus give good bounds for the 2-D strip packing problem.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128972156","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185424
A. Gál
It is proved that the reliable computation of any Boolean function with, sensitivity s requires Omega (s log s) gates if the gates of the circuit fail independently with a fixed positive probability. The Omega (s log s) bound holds even if s is the block sensitivity instead of the sensitivity of the Boolean function. Some open problems are mentioned.<>
证明了当电路的门以固定的正概率独立失效时,任何灵敏度为s的布尔函数的可靠计算都需要ω (s log s)门。即使s是块灵敏度而不是布尔函数的灵敏度,ω (s log s)边界也成立。文中还提到了一些尚未解决的问题。
{"title":"Lower bounds for the complexity of reliable Boolean circuits with noisy gates","authors":"A. Gál","doi":"10.1109/SFCS.1991.185424","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185424","url":null,"abstract":"It is proved that the reliable computation of any Boolean function with, sensitivity s requires Omega (s log s) gates if the gates of the circuit fail independently with a fixed positive probability. The Omega (s log s) bound holds even if s is the block sensitivity instead of the sensitivity of the Boolean function. Some open problems are mentioned.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116005970","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185354
Sanjoy Baruah, G. Koren, B. Mishra, A. Raghunathan, L. Rosier, D. Shasha
The preemptive scheduling of sporadic tasks on a uniprocessor is considered. A task may arrive at any time, and is characterized by a value that reflects its importance, an execution time that is the amount of processor time needed to completely execute the task, and a deadline by which the task is to complete execution. The goal is to maximize the sum of the values of the completed tasks. An online scheduling algorithm that achieves optimal performance when the system is underloaded and provides a nontrivial performance guarantee when the system is overloaded is designed. The algorithm is implemented using simple data structures to run at a cost of O(log n) time per task, where n bounds the number of tasks in the system at any instant. Upper bounds on the best performance guarantee obtainable by an online algorithm in a variety of settings are derived.<>
{"title":"On-line scheduling in the presence of overload","authors":"Sanjoy Baruah, G. Koren, B. Mishra, A. Raghunathan, L. Rosier, D. Shasha","doi":"10.1109/SFCS.1991.185354","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185354","url":null,"abstract":"The preemptive scheduling of sporadic tasks on a uniprocessor is considered. A task may arrive at any time, and is characterized by a value that reflects its importance, an execution time that is the amount of processor time needed to completely execute the task, and a deadline by which the task is to complete execution. The goal is to maximize the sum of the values of the completed tasks. An online scheduling algorithm that achieves optimal performance when the system is underloaded and provides a nontrivial performance guarantee when the system is overloaded is designed. The algorithm is implemented using simple data structures to run at a cost of O(log n) time per task, where n bounds the number of tasks in the system at any instant. Upper bounds on the best performance guarantee obtainable by an online algorithm in a variety of settings are derived.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115156911","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185396
Moshe Morgenstern
The first known direct construction for linear families of bounded concentrators is given. The construction is explicit, and the results are simple natural bounded concentrators.<>
给出了有界集中器线性族的第一个已知的直接构造。构造是显式的,结果是简单的自然有界集中器
{"title":"Explicit construction of natural bounded concentrators","authors":"Moshe Morgenstern","doi":"10.1109/SFCS.1991.185396","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185396","url":null,"abstract":"The first known direct construction for linear families of bounded concentrators is given. The construction is explicit, and the results are simple natural bounded concentrators.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127236251","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185439
M. Goodrich
A framework is presented for designing parallel algorithms that may ignore processor allocation. A number of fast approximation algorithms are developed, and it is shown how to use these algorithms to simulate any algorithm that fits this framework in a work-preserving fashion on a randomized CRCW PRAM. Several applications of the approach to parallel computational geometry are given.<>
{"title":"Using approximation algorithms to design parallel algorithms that may ignore processor allocation","authors":"M. Goodrich","doi":"10.1109/SFCS.1991.185439","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185439","url":null,"abstract":"A framework is presented for designing parallel algorithms that may ignore processor allocation. A number of fast approximation algorithms are developed, and it is shown how to use these algorithms to simulate any algorithm that fits this framework in a work-preserving fashion on a randomized CRCW PRAM. Several applications of the approach to parallel computational geometry are given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125565043","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185384
J. Radhakrishnan
The computation of threshold functions using formulas over the basis (AND, OR, NOT) is considered. It is shown that every monotone formula that computes the threshold function T/sub k//sup n/2>
{"title":"Better bounds for threshold formulas","authors":"J. Radhakrishnan","doi":"10.1109/SFCS.1991.185384","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185384","url":null,"abstract":"The computation of threshold functions using formulas over the basis (AND, OR, NOT) is considered. It is shown that every monotone formula that computes the threshold function T/sub k//sup n/2<or=k<or=n/2, has size Omega (nk log (n/(k-1))). The same lower bound is shown to hold even in the stronger monotone contact networks model. Nearly optimal bounds on the size of Sigma Pi Sigma formulas computing T/sub k//sup n/ for small k are also shown.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127467916","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185437
Donald B. Johnson, P. Metaxas
Computing the connected components of an undirected graph G=(V, E) on mod V mod =n vertices and mod E mod =m edges is addressed. An efficient and simple algorithm that runs in O(lg/sup 3/2/ n) time using n+m CREW processors is presented.<>
计算无向图G=(V, E)在V mod =n个顶点和E mod =m条边上的连通分量。提出了一种使用n+m CREW处理器,运行时间为O(lg/sup 3/2/ n)的高效简单算法。
{"title":"Connected components in O(lg/sup 3/2 mod V/ mod ) parallel time for the CREW PRAM","authors":"Donald B. Johnson, P. Metaxas","doi":"10.1109/SFCS.1991.185437","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185437","url":null,"abstract":"Computing the connected components of an undirected graph G=(V, E) on mod V mod =n vertices and mod E mod =m edges is addressed. An efficient and simple algorithm that runs in O(lg/sup 3/2/ n) time using n+m CREW processors is presented.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121524316","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185410
D. Eppstein
Linear programming optimizations on the intersection of k polyhedra in R/sup 3/, represented by their outer recursive decompositions, are performed in expected time O(k log k log n+ square root k log k log/sup 3/ n). This result is used to derive efficient algorithms for dynamic linear programming problems ill which constraints are inserted and deleted, and queries must optimize specified objective functions. As an application, an improved solution to the planar 2-center problem, is described.<>
在R/sup 3/中k个多面体的交点上,用它们的外部递归分解表示线性规划优化,在期望时间O(k log k log n+平方根k log k log/sup 3/ n)内完成了线性规划优化。这一结果用于导出动态线性规划问题的有效算法,这些问题需要插入和删除约束,查询必须优化指定的目标函数。作为应用,本文描述了平面二中心问题的一种改进解
{"title":"Dynamic three-dimensional linear programming","authors":"D. Eppstein","doi":"10.1109/SFCS.1991.185410","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185410","url":null,"abstract":"Linear programming optimizations on the intersection of k polyhedra in R/sup 3/, represented by their outer recursive decompositions, are performed in expected time O(k log k log n+ square root k log k log/sup 3/ n). This result is used to derive efficient algorithms for dynamic linear programming problems ill which constraints are inserted and deleted, and queries must optimize specified objective functions. As an application, an improved solution to the planar 2-center problem, is described.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125648995","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185417
G. Miller, S. Teng, S. Vavasis
A class of graphs called k-overlap graphs is proposed. Special cases of k-overlap graphs include planar graphs, k-nearest neighbor graphs, and earlier classes of graphs associated with finite element methods. A separator bound is proved for k-overlap graphs embedded in d dimensions. The result unifies several earlier separator results. All the arguments are based on geometric properties of embedding. The separator bounds come with randomized linear-time and randomized NC algorithms. Moreover, the bounds are the best possible up to the leading term.<>
{"title":"A unified geometric approach to graph separators","authors":"G. Miller, S. Teng, S. Vavasis","doi":"10.1109/SFCS.1991.185417","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185417","url":null,"abstract":"A class of graphs called k-overlap graphs is proposed. Special cases of k-overlap graphs include planar graphs, k-nearest neighbor graphs, and earlier classes of graphs associated with finite element methods. A separator bound is proved for k-overlap graphs embedded in d dimensions. The result unifies several earlier separator results. All the arguments are based on geometric properties of embedding. The separator bounds come with randomized linear-time and randomized NC algorithms. Moreover, the bounds are the best possible up to the leading term.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122229727","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}