Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185371
K. Mulmuley
The use of randomization in dynamic search structures by means of a technique called dynamic sampling is investigated. In particular, an efficient algorithm for dynamic (logarithmic time) point location in 3-D partitions induced by a set of possibly interesting polygons in R/sup 3/ is given. The expected running time of the algorithm on a random sequence of updates is close to optimal. Efficient algorithms for dynamic nearest-k-neighbor queries and half space range queries in R/sup d/ are also given.<>
{"title":"Randomized multidimensional search trees: further results in dynamic sampling","authors":"K. Mulmuley","doi":"10.1109/SFCS.1991.185371","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185371","url":null,"abstract":"The use of randomization in dynamic search structures by means of a technique called dynamic sampling is investigated. In particular, an efficient algorithm for dynamic (logarithmic time) point location in 3-D partitions induced by a set of possibly interesting polygons in R/sup 3/ is given. The expected running time of the algorithm on a random sequence of updates is close to optimal. Efficient algorithms for dynamic nearest-k-neighbor queries and half space range queries in R/sup d/ are also given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"40 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":"129497197","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.1991.185440
Hillel Gazit
A deterministic parallel algorithm for determining whether two planar graphs are isomorphic is presented. The algorithm needs O(log n) separators that have to be computed one after the other. The running time is T=O(log/sup 3/ n) time for finding separators, and the processors count is n/sup 1.5/ log n/T. It is also shown that every planar graph has a separator, and a parallel algorithm for finding the separator is given.<>
{"title":"A deterministic parallel algorithm for planar graphs isomorphism","authors":"Hillel Gazit","doi":"10.1109/SFCS.1991.185440","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185440","url":null,"abstract":"A deterministic parallel algorithm for determining whether two planar graphs are isomorphic is presented. The algorithm needs O(log n) separators that have to be computed one after the other. The running time is T=O(log/sup 3/ n) time for finding separators, and the processors count is n/sup 1.5/ log n/T. It is also shown that every planar graph has a separator, and a parallel algorithm for finding the separator is given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"330 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":"134299616","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.1991.185448
Matthias Krause, S. Waack
An exponential lower bound for depth two circuits with arbitrary symmetric gates in the bottom level and with a MOD/sub m/-gate in the top level is proved. This solves a problem posed by R. Smolensky (1990). The method uses the variation rank of communication matrices. A variant of this method is used for deriving lower bounds for the size of depth-two circuits having a threshold gate at the top.<>
{"title":"Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in","authors":"Matthias Krause, S. Waack","doi":"10.1109/SFCS.1991.185448","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185448","url":null,"abstract":"An exponential lower bound for depth two circuits with arbitrary symmetric gates in the bottom level and with a MOD/sub m/-gate in the top level is proved. This solves a problem posed by R. Smolensky (1990). The method uses the variation rank of communication matrices. A variant of this method is used for deriving lower bounds for the size of depth-two circuits having a threshold gate at the top.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"42 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":"116456362","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.1991.185415
M. Herlihy, N. Shavit, Orli Waarts
The linearizable counting problem requires asynchronous concurrent processes to assign themselves successive values so that the order of the values assigned reflects the real-time order in which they were requested. It is shown that the problem can be solved without funneling all processes through a common memory location. Two new constructions for linearizable counting networks, data structures that solve the linearizable counting problem, are given. The first construction is nonblocking: some process takes a value after O(n) network gates have been traversed. The second construction is wait-free: it guarantees that each process takes a value after it traverses O(wn) gates, where w is a parameter affecting contention. It is shown that in any nonblocking or wait-free linearizable counting network, processes must traverse an average of Omega (n) gates, and so the constructions are close to optimal. A simpler and more efficient network is constructed by giving up the robustness requirements and allowing processes to wait for one another.<>
{"title":"Low contention linearizable counting","authors":"M. Herlihy, N. Shavit, Orli Waarts","doi":"10.1109/SFCS.1991.185415","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185415","url":null,"abstract":"The linearizable counting problem requires asynchronous concurrent processes to assign themselves successive values so that the order of the values assigned reflects the real-time order in which they were requested. It is shown that the problem can be solved without funneling all processes through a common memory location. Two new constructions for linearizable counting networks, data structures that solve the linearizable counting problem, are given. The first construction is nonblocking: some process takes a value after O(n) network gates have been traversed. The second construction is wait-free: it guarantees that each process takes a value after it traverses O(wn) gates, where w is a parameter affecting contention. It is shown that in any nonblocking or wait-free linearizable counting network, processes must traverse an average of Omega (n) gates, and so the constructions are close to optimal. A simpler and more efficient network is constructed by giving up the robustness requirements and allowing processes to wait for one another.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"96 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":"133805220","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.1991.185383
R. Klein
A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with onboard vision, a strategy for finding a short path from s to g in a street not known in advance is described, and it is proved that the length of the path created does not exceed 1+3 pi /2 times the length of the shortest path from s to g. Experiments suggest that the strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.<>
如果从s到g的两个边界链相互弱可见，则具有两个不同顶点s和g的多边形称为街道。对于具有板载视觉的移动机器人，描述了在事先未知的街道上寻找从s到g的短路径的策略，并证明了所创建的路径长度不超过从s到g的最短路径长度的1+3 pi /2倍。实验表明，该策略比这好得多，因为尚未观察到大于1.8的比率。对于每个策略可能被迫产生的相对弯路，这是1.41的下界。
{"title":"Walking an unknown street with bounded detour","authors":"R. Klein","doi":"10.1109/SFCS.1991.185383","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185383","url":null,"abstract":"A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with onboard vision, a strategy for finding a short path from s to g in a street not known in advance is described, and it is proved that the length of the path created does not exceed 1+3 pi /2 times the length of the shortest path from s to g. Experiments suggest that the strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"58 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":"124504723","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.1991.185449
R. Beigel, J. Tarui
It has been shown by A. Yao (1990) that every language in ACC is recognized by a sequence of depth-2 probabilistic circuits with a symmetric gate at the root and n/sup polylog/(n) AND gates of fan-in polylog (n) at the leaves. The authors simplify Yao's proof and strengthen his results: every language in ACC is recognized by a sequence of depth-2 deterministic circuits with a symmetric gate at the root and n/sup polylog/(n) AND gates of fan-in polylog(n) at the leaves. They also analyze and improve modulus-amplifying polynomials constructed by S. Toda (1989) and Yao: this yields smaller circuits in Yao's and the present results on ACC.<>
a . Yao(1990)已经证明，ACC中的每种语言都是通过深度为2的概率电路序列来识别的，这些电路在根处具有对称门，在叶处具有n/sup polylog/(n)扇入polylog (n)的与门。作者简化了Yao的证明并加强了他的结果:ACC中的每种语言都被一个深度为2的确定性电路序列识别，该电路在根处具有对称门，在叶处具有n/sup polylog/(n)与扇入(n) polylog的门。他们还分析和改进了S. Toda(1989)和Yao构造的模放大多项式:这在Yao的电路和ACC上产生了更小的电路。
{"title":"On ACC (circuit complexity)","authors":"R. Beigel, J. Tarui","doi":"10.1109/SFCS.1991.185449","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185449","url":null,"abstract":"It has been shown by A. Yao (1990) that every language in ACC is recognized by a sequence of depth-2 probabilistic circuits with a symmetric gate at the root and n/sup polylog/(n) AND gates of fan-in polylog (n) at the leaves. The authors simplify Yao's proof and strengthen his results: every language in ACC is recognized by a sequence of depth-2 deterministic circuits with a symmetric gate at the root and n/sup polylog/(n) AND gates of fan-in polylog(n) at the leaves. They also analyze and improve modulus-amplifying polynomials constructed by S. Toda (1989) and Yao: this yields smaller circuits in Yao's and the present results on ACC.<<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":"130191162","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.1991.185411
Serge A. Plotkin, D. Shmoys, É. Tardos
Fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems, are presented. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. The algorithms are based on a Lagrangian relaxation technique, and an important result is a theoretical analysis of the running time of a Lagrangian relaxation based algorithm. Several applications of the algorithms are presented.<>
{"title":"Fast approximation algorithms for fractional packing and covering problems","authors":"Serge A. Plotkin, D. Shmoys, É. Tardos","doi":"10.1109/SFCS.1991.185411","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185411","url":null,"abstract":"Fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems, are presented. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. The algorithms are based on a Lagrangian relaxation technique, and an important result is a theoretical analysis of the running time of a Lagrangian relaxation based algorithm. Several applications of the algorithms are presented.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"4 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":"125422178","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.1991.185392
E. Emerson, C. Jutla
It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the mu-calculus, the equivalence provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results. It is also shown how mu-calculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms.<>
{"title":"Tree automata, mu-calculus and determinacy","authors":"E. Emerson, C. Jutla","doi":"10.1109/SFCS.1991.185392","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185392","url":null,"abstract":"It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the mu-calculus, the equivalence provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results. It is also shown how mu-calculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"23 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":"125432036","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.1991.185433
D. Grigoriev, Marek Karpinski
The authors design the first polynomial time (for an arbitrary and fixed field GF(q)) ( in , delta )-approximation algorithm for the number of zeros of arbitrary polynomial f(x/sub 1/. . . x/sub n/) over GF(q). It gives the first efficient method for estimating the number of zeros and nonzeros of multivariate polynomials over small finite fields other than GF(2) (like GF(3)), the case important for various circuit approximation techniques. The algorithm is based on the estimation of the number of zeros of an arbitrary polynomial f(x/sub 1/. . .,x/sub n/) over GF(q) in the function of the number m of its terms. The bounding ratio is proved to be m/sup (q-1)/log/sup q/.<>
{"title":"An approximation algorithm for the number of zeros or arbitrary polynomials over GF(q)","authors":"D. Grigoriev, Marek Karpinski","doi":"10.1109/SFCS.1991.185433","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185433","url":null,"abstract":"The authors design the first polynomial time (for an arbitrary and fixed field GF(q)) ( in , delta )-approximation algorithm for the number of zeros of arbitrary polynomial f(x/sub 1/. . . x/sub n/) over GF(q). It gives the first efficient method for estimating the number of zeros and nonzeros of multivariate polynomials over small finite fields other than GF(2) (like GF(3)), the case important for various circuit approximation techniques. The algorithm is based on the estimation of the number of zeros of an arbitrary polynomial f(x/sub 1/. . .,x/sub n/) over GF(q) in the function of the number m of its terms. The bounding ratio is proved to be m/sup (q-1)/log/sup q/.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"17 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":"128711471","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.1991.185361
D. Shmoys, J. Wein, David P. Williamson
The authors study the problem of scheduling jobs on parallel machines when the existence of a job is not known until an unknown release date and the processing requirement of a job is not known until the job is processed to completion. They demonstrate two general algorithmic techniques for converting existing polynomial-time algorithms that require complete knowledge about the input data into algorithms that need less advance knowledge. They prove information-theoretic lower bounds on the lengths of online schedules for several basic parallel machine models and then show that the algorithms construct schedules with lengths that either match or come within a constant factor of the lower bounds.<>
{"title":"Scheduling parallel machines on-line","authors":"D. Shmoys, J. Wein, David P. Williamson","doi":"10.1109/SFCS.1991.185361","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185361","url":null,"abstract":"The authors study the problem of scheduling jobs on parallel machines when the existence of a job is not known until an unknown release date and the processing requirement of a job is not known until the job is processed to completion. They demonstrate two general algorithmic techniques for converting existing polynomial-time algorithms that require complete knowledge about the input data into algorithms that need less advance knowledge. They prove information-theoretic lower bounds on the lengths of online schedules for several basic parallel machine models and then show that the algorithms construct schedules with lengths that either match or come within a constant factor of the lower bounds.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"44 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":"130250574","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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