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Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)最新文献

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The access network design problem 接入网的设计问题
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743427
M. Andrews, Lisa Zhang
{"title":"The access network design problem","authors":"M. Andrews, Lisa Zhang","doi":"10.1109/SFCS.1998.743427","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743427","url":null,"abstract":"We consider the problem of designing a minimum cost access network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types are available for leasing or buying. Some trunk-types have a high initial overhead cost but a low cost per unit bandwidth. Others have a low overhead cost but a high cost per unit bandwidth. When the central core is given, we show how to construct an access network whose cost is within O(K/sup 2/) of optimal, under weak assumptions on the cost structure. In contrast with previous bounds, this bound is independent of the network and the traffic. Typically, the value of K is small. Our approach uses a linear programming relaxation and is motivated by a rounding technique of Shmoys, Tardos and Aardal (1997). Our techniques extend to a more complex situation in which the core is not given a priori. In this case we aim to minimize the switch cost of the core in addition to the trunk cost of the access network. We provide the same performance bound.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124525659","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: 76
A characterization of NC by tree recurrence NC的树递归表征
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743522
D. Leivant
{"title":"A characterization of NC by tree recurrence","authors":"D. Leivant","doi":"10.1109/SFCS.1998.743522","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743522","url":null,"abstract":"We show that a boolean valued function is in NC if it is defined by ramified schematic recurrence over trees. This machine-independent characterization uses no initial functions other than basic tree operations, and no bounding conditions on the recurrence. Aside from its technical interest, our result evidences the foundational nature of NC, thereby illustrating the merits of implicit (i.e. machine independent) computational complexity theory.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114895517","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: 21
Quantum cryptography with imperfect apparatus 设备不完善的量子密码术
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-09-15 DOI: 10.1109/SFCS.1998.743501
D. Mayers, A. Yao
{"title":"Quantum cryptography with imperfect apparatus","authors":"D. Mayers, A. Yao","doi":"10.1109/SFCS.1998.743501","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743501","url":null,"abstract":"Quantum key distribution, first proposed by C.H. Bennett and G. Brassard (1984), provides a possible key distribution scheme whose security depends only on the quantum laws of physics. So far the protocol has been proved secure even under channel noise and detector faults of the receiver but is vulnerable if the photon source used is imperfect. In this paper we propose and give a concrete design for a new concept, self-checking source, which requires the manufacturer of the photon source to provide certain tests; these tests are designed such that, if passed, the source is guaranteed to be adequate for the security of the quantum key distribution protocol, even though the testing devices may not be built to the original specification. The main mathematical result is a structural theorem which states that, for any state in a Hilbert space, if certain EPR-type equations are satisfied, the state must be essentially the orthogonal sum of EPR pairs.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130986527","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: 407
Marked ancestor problems 明显的祖先问题
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-09-13 DOI: 10.1109/SFCS.1998.743504
Stephen Alstrup, T. Husfeldt, Theis Rauhe
{"title":"Marked ancestor problems","authors":"Stephen Alstrup, T. Husfeldt, Theis Rauhe","doi":"10.1109/SFCS.1998.743504","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743504","url":null,"abstract":"Consider a rooted tree whose nodes can be in two states: marked or unmarked. The marked ancestor problem is to maintain a data structure with the following operations: mark(v) marks node v: unmark(v) removes any marks from node v; firstmarked(v) returns the first marked node on the path from v to the root. We show tight upper and lower bounds for the marked ancestor problem. The lower bounds are proved in the cell probe model, the algorithms run on a unit-cost RAM. As easy corollaries we prove (often optimal) lower bounds on a number of problems. These include planar range searching, including the existential or emptiness problem, priority search trees static tree union-find, and several problems from dynamic computational geometry, including segment intersection, interval maintenance, and ray shooting in the plane. Our upper bounds improve algorithms from various fields, including coloured ancestor problems and maintenance of balanced parentheses.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132512587","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: 127
1-way quantum finite automata: strengths, weaknesses and generalizations 单向量子有限自动机:优点、缺点和推广
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-02-24 DOI: 10.1109/SFCS.1998.743469
A. Ambainis, R. Freivalds
{"title":"1-way quantum finite automata: strengths, weaknesses and generalizations","authors":"A. Ambainis, R. Freivalds","doi":"10.1109/SFCS.1998.743469","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743469","url":null,"abstract":"We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton. We think that this construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126295322","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: 269
Quantum lower bounds by polynomials 多项式的量子下界
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-02-18 DOI: 10.1109/SFCS.1998.743485
R. Beals, H. Buhrman, R. Cleve, M. Mosca, R. D. Wolf
{"title":"Quantum lower bounds by polynomials","authors":"R. Beals, H. Buhrman, R. Cleve, M. Mosca, R. D. Wolf","doi":"10.1109/SFCS.1998.743485","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743485","url":null,"abstract":"We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions (i.e. problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function: if a quantum algorithm computes some total Boolean function f with bounded-error using T black-box queries then there is a classical deterministic algorithm that computes f exactly with O(T/sup 6/) queries. We also give asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings. Finally, we give new precise bounds for AND, OR, and PARITY. Our results are a quantum extension of the so-called polynomial method, which has been successfully applied in classical complexity theory, and also a quantum extension of results by Nisan about a polynomial relationship between randomized and deterministic decision tree complexity.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116845645","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: 772
Optimal time-space trade-offs for sorting 排序的最佳时空权衡
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-01-10 DOI: 10.1109/SFCS.1998.743455
J. Pagter, Theis Rauhe
{"title":"Optimal time-space trade-offs for sorting","authors":"J. Pagter, Theis Rauhe","doi":"10.1109/SFCS.1998.743455","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743455","url":null,"abstract":"We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem. P. Beame (1991) has shown a lower bound of /spl Omega/(n/sup 2/) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n/sup 2/ log n) due to G.N. Frederickson (1987). Since then, no progress has been made towards tightening this gap. The main contribution of this paper is a comparison based sorting algorithm which closes the gap by meeting the lower bound of Beame. The time-space product O(n/sup 2/) upper bound holds for the full range of space bounds between log n and n/log n. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128598693","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: 69
Multiplicative complexity of Taylor shifts and a new twist of the substitution method 泰勒移位的乘法复杂度和替换法的一种新方法
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1900-01-01 DOI: 10.1109/SFCS.1998.743445
A. Schonhage
{"title":"Multiplicative complexity of Taylor shifts and a new twist of the substitution method","authors":"A. Schonhage","doi":"10.1109/SFCS.1998.743445","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743445","url":null,"abstract":"Let C/sub n/=C/sub n/(K) denote the minimum number of essential multiplications/divisions required for shifting a general n-th degree polynomial A(t)=/spl Sigma/a/sub i/t/sup i/ to some new origin x, which means to compute the coefficients b/sub k/ of the Taylor expansion A(x+t)=B(t)=/spl Sigma/b/sub k/t/sup k/ as elements of K(x,a/sub 0/,...,a/sub n/) with indeterminates a/sub i/ and x over some ground field K. For K of characteristic zero, a new refined version of the substitution method combined with a dimension argument enables us to prove C/sub n//spl ges/n+[n/2]-1 opposed to an upper bound of C/sub n//spl les/2n+[n/2]-4 valid for all n/spl ges/3.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123308800","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: 2
Bivariate polynomial multiplication 二元多项式乘法
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1900-01-01 DOI: 10.1109/SFCS.1998.743442
M. Blaser
{"title":"Bivariate polynomial multiplication","authors":"M. Blaser","doi":"10.1109/SFCS.1998.743442","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743442","url":null,"abstract":"We study the multiplicative complexity and the rank of the multiplication in the local algebras R/sub m,n/=k[x,y]/(x/sup m+1/,y/sup n+1/) and T/sub n/=k[x,y]/(x/sup n+1/,x/sup n/y,...,y/sup n+1/) of bivariate polynomials. We obtain the lower bounds (21/3-0(1))/spl middot/dim R/sub m,n/, and (2 1/2 -0(1))/spl middot/dim T/sub n/ for the multiplicative complexity of the multiplication in R/sub m,n/ and T/sub n/, respectively. On the other hand, we derive the upper bounds 3/spl middot/dim T/sub n/-2n-2 and 3/spl middot/dim R/sub m.n/-m-n-3 for the rank of the multiplication in T/sub n/ and R/sub m,n/, respectively, provided that the ground field k admits \"fast\" univariate polynomial multiplication mod x/sup N/-1. Our results are also applicable to arbitrary finite dimensional algebras of truncated bivariate polynomials k[x,y]/I, where the ideal I=(x(d/sub 0/+1),x(d/sub 1/+1)y,...,x(d/sub n/+1)y/sup n/,y/sup n+1/) is described by a degree pattern d/sub 0//spl ges/d/sub 1//spl ges//spl middot//spl middot//spl middot//spl ges/d/sub n//spl ges/0.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116622016","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: 4
Quantum oracle interrogation: getting all information for almost half the price 量子甲骨文审讯:以几乎一半的价格获得所有信息
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1900-01-01 DOI: 10.1109/SFCS.1998.743486
W. van Dam
{"title":"Quantum oracle interrogation: getting all information for almost half the price","authors":"W. van Dam","doi":"10.1109/SFCS.1998.743486","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743486","url":null,"abstract":"Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+/spl radic/N calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+/spl radic/N queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(/spl radic/N) oracle queries. In the second part of the article 'approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127187752","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: 87
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