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Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science最新文献

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Geometric discrepancy revisited 重新审视几何差异
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366848
B. Chazelle
{"title":"Geometric discrepancy revisited","authors":"B. Chazelle","doi":"10.1109/SFCS.1993.366848","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366848","url":null,"abstract":"Discrepancy theory addresses the general issue of approximating one measure by another one. Originally an offshoot of diophantine approximation theory, the area has expanded into applied mathematics, and now, computer science. Besides providing the theoretical foundation for sampling, it holds some of the keys to understanding the computational power of randomization. A few applications of discrepancy theory are listed. We give elementary algorithms for estimating the discrepancy between various measures arising in practice. We also present a general technique for proving discrepancy lower bounds.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130316779","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}
引用次数: 16
Sensitive functions and approximate problems 敏感函数与近似问题
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366868
S. Chaudhuri
{"title":"Sensitive functions and approximate problems","authors":"S. Chaudhuri","doi":"10.1109/SFCS.1993.366868","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366868","url":null,"abstract":"We investigate properties of functions that are good measures of the CRCW PRAM complexity of computing them. While the block sensitivity is known to be a good measure of the CREW PRAM complexity, no such measure is known for CRCW PRAMs. We show that the complexity of computing a function is related to its everywhere sensitivity, introduced by Vishkin and Wigderson (1985). Specifically we show that the time required to compute a function f:D/sup n//spl rarr/R of everywhere sensitivity es(f) with P/spl ges/n processors and unbounded memory is /spl Omega/(log[log es(f)/(log 4P|D|- log es(f))]). This improves previous results of Azar (1992), and Vishkin and Wigderson. We use this lower bound to derive new lower bounds for some approximate problems. These problems can often be solved faster than their exact counterparts and for many applications, it is sufficient to solve the approximate problem. We show that approximate selection requires time /spl Omega/(log[log n/log k]) with kn, processors and approximate counting with accuracy /spl lambda//spl ges/2 requires time /spl Omega/(log[log n/(log k+log /spl lambda/)]) with kn processors. In particular, for constant accuracy, no lower bounds were known for these problems.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114391983","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}
引用次数: 9
The complexity and distribution of hard problems 难题的复杂性和分布
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366869
D. Juedes, J. H. Lutz
{"title":"The complexity and distribution of hard problems","authors":"D. Juedes, J. H. Lutz","doi":"10.1109/SFCS.1993.366869","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366869","url":null,"abstract":"Measure-theoretic aspects of the /spl les//sub m//sup P/-reducibility structure of exponential time complexity classes E=DTIME(2/sup linear/) and E/sub 2/=DTIME(2/sup polynomial/) are investigated. Particular attention is given to the complexity (measured by the size of complexity cores) and distribution (abundance in the sense of measure) of languages that are /spl les//sub m//sup P/-hard for E and other complexity classes. Tight upper and lower bounds on the size of complexity cores of hard languages are derived. The upper bounds say that the /spl les//sub m//sup P/-hard languages for E are unusually simple in, the sense that they have smaller complexity cores than most languages in E. It follows that the /spl les//sub m//sup P/-complete languages for E form a measure 0 subset of E (and similarly in E/sub 2/). This latter fact is seen to be a special case of a more general theorem, namely, that every /spl les//sub m//sup P/-degree (e.g. the degree of all /spl les//sub m//sup P/-complete languages for NP) has measure 0 in E and in E/sub 2/.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122071021","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}
引用次数: 96
A linear-processor polylog-time algorithm for shortest paths in planar graphs 平面图中最短路径的线性处理器多对数时间算法
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366861
P. Klein, Sairam Subramanian
{"title":"A linear-processor polylog-time algorithm for shortest paths in planar graphs","authors":"P. Klein, Sairam Subramanian","doi":"10.1109/SFCS.1993.366861","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366861","url":null,"abstract":"We give an algorithm requiring polylog time and a linear number of processors to solve single-source shortest paths in directed planar graphs, bounded-genus graphs, and 2-dimensional overlap graphs. More generally, the algorithm works for any graph provided with a decomposition tree constructed using size-O(/spl radic/n polylog n) separators.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127078065","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}
引用次数: 53
Random sampling in matroids, with applications to graph connectivity and minimum spanning trees 在拟阵中的随机抽样，与应用图的连通性和最小生成树
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366879
D.R. Karker
{"title":"Random sampling in matroids, with applications to graph connectivity and minimum spanning trees","authors":"D.R. Karker","doi":"10.1109/SFCS.1993.366879","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366879","url":null,"abstract":"Random sampling is a powerful way to gather information about a group by considering only a small part of it. We give a paradigm for applying this technique to optimization problems, and demonstrate its effectiveness on matroids. Matroids abstractly model many optimization problems that can be solved by greedy methods, such as the minimum spanning tree (MST) problem. Our results have several applications. We give an algorithm that uses simple data structures to construct an MST in O(m+n log n) time. We give bounds on the connectivity (minimum cut) of a graph suffering random edge failures. We give fast algorithms for packing matroid bases, with particular attention to packing spanning trees in graphs.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125103895","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}
引用次数: 24
General bounds on statistical query learning and PAC learning with noise via hypothesis boosting 基于假设增强的统计查询学习和带有噪声的PAC学习的一般界限
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366859
J. Aslam, Scott E. Decatur
{"title":"General bounds on statistical query learning and PAC learning with noise via hypothesis boosting","authors":"J. Aslam, Scott E. Decatur","doi":"10.1109/SFCS.1993.366859","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366859","url":null,"abstract":"We derive general bounds on the complexity of learning in the statistical query model and in the PAC model with classification noise. We do so by considering the problem of boosting the accuracy of weak learning algorithms which fall within the statistical query model. This new model was introduced by M. Kearns (1993) to provide a general framework for efficient PAC learning in the presence of classification noise.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128788567","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}
引用次数: 68
The union of convex polyhedra in three dimensions 三维凸多面体的结合
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366835
B. Aronov, M. Sharir, Boaz Tagansky
{"title":"The union of convex polyhedra in three dimensions","authors":"B. Aronov, M. Sharir, Boaz Tagansky","doi":"10.1109/SFCS.1993.366835","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366835","url":null,"abstract":"We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k/sup 3/+knlog/sup 2/ k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k/sup 3/+knlog/sup 3/ k) expected time.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130873181","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}
引用次数: 72
A tight lower bound for k-set agreement k集一致的紧下界
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366866
S. Chaudhuri, M. Herlihy, N. Lynch, M. Tuttle
{"title":"A tight lower bound for k-set agreement","authors":"S. Chaudhuri, M. Herlihy, N. Lynch, M. Tuttle","doi":"10.1109/SFCS.1993.366866","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366866","url":null,"abstract":"We prove tight bounds on the time needed to solve k-set agreement, a natural generalization of consensus. We analyze this problem in a synchronous, message-passing model where processors fail by crashing. We prove a lower bound of [f/k]+1 rounds of communication for solutions to k-set agreement that tolerate f failures. This bound is tight, and shows that there is an inherent tradeoff between the running time, the degree of coordination required, and the number of faults tolerated, even in idealized models like the synchronous model. The proof of this result is interesting because it is a geometric combination of other well-known proof techniques.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132475964","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}
引用次数: 42
Gates accept concurrent behavior 盖茨接受并发行为
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366881
Vineet Gupta, V. Pratt
{"title":"Gates accept concurrent behavior","authors":"Vineet Gupta, V. Pratt","doi":"10.1109/SFCS.1993.366881","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366881","url":null,"abstract":"We represent concurrent processes as Boolean propositions or gates, cast in the role of accepters of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essentially that of linear logic, with its morphisms being consequence-preserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132076033","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}
引用次数: 54
Directed vs. undirected monotone contact networks for threshold functions 阈值函数的有向与无向单调接触网络
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366826
M. Halldórsson, J. Radhakrishnan, K. Subrahmanyam
{"title":"Directed vs. undirected monotone contact networks for threshold functions","authors":"M. Halldórsson, J. Radhakrishnan, K. Subrahmanyam","doi":"10.1109/SFCS.1993.366826","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366826","url":null,"abstract":"We consider the problem of computing threshold functions using directed and undirected monotone contact networks. Our main results are the following. First, we show that there exist directed monotone contact networks that compute T/sub k//sup n/, 2/spl les/k/spl les/n-1, of size O(k(n-k+2)log(n-k+2)). This bound is almost optimal for small thresholds, since there exists an /spl Omega/(knlog (n/(k-1))) lower bound. Our networks are described explicitly; the previously best upper bound known, obtained from the undirected networks of Dubiner and Zwick, used non-constructive arguments and gave directed networks of size O(k/sup 3.99/nlog n). Second, we show a lower bound of O(nlogloglog n) on the size of undirected monotone contact networks computing T/sub n-1//sup n/, improving the 2(n-1) lower bound of Markov. Combined with our upper bound result, this shows that directed monotone contact networks compute some threshold functions more easily than undirected networks.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122586138","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}
引用次数: 8
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