B. Awerbuch, S. Kutten, Y. Mansour, B. Patt-Shamir, G. Varghese
In the network synchronization model, each node maintains a local pulse counter such that the advance of the pulse numbers simulates the advance of a clock in a synchronous network. In this paper we present a tame optimai sel&stabilizing scheme for network synchronization. Our construction has two parts. First, we give a simple rule by which each node can compute its pulse number as a function of its neighbors’ pulse numbers. This rule stabilizes in time bounded by t?te diameter of the network, it does not revoke global operations, and does not require any additional memory space. However, this rule works correctly only if the pulse numbers may grow unfoundedly. The second part of the construction (whzch is of independent interest in its own right) takes care of this problem. Specifically, we present the jirst self-stabilizing reset procedure that stabilizes in tzme proportional to the diameter of the network. This procedure can be combined with unbounded-register protocols to yield bounded-register algorithms. “Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86K-01 71, NSF contract CCR861 1442, DARPA contract NOOO1489-J-1988, and a special grant from IBM. t IBM T.J. Watson Research Center. $Tel-Aviv University and IBM T.J. Watson Research Center. $Lab. for Computer Science, MIT. Research partly done while visiting IBM T.J. Watson Research Center. Supported in part by DARPA contracts NOOO1 4-92J-4o33 and NOOO1492-J-1799, ONR contract NOOO14-91-J-1O46, and NSF contract 8915206-CCR. !IDEG, 55o King Street, Llttleton, MA 01460. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice ia given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ J993 AG~ Q-89~9J-59 J-7/93 /QQQ51Q652,.. $J.~Q
{"title":"Time optimal self-stabilizing synchronization","authors":"B. Awerbuch, S. Kutten, Y. Mansour, B. Patt-Shamir, G. Varghese","doi":"10.1145/167088.167256","DOIUrl":"https://doi.org/10.1145/167088.167256","url":null,"abstract":"In the network synchronization model, each node maintains a local pulse counter such that the advance of the pulse numbers simulates the advance of a clock in a synchronous network. In this paper we present a tame optimai sel&stabilizing scheme for network synchronization. Our construction has two parts. First, we give a simple rule by which each node can compute its pulse number as a function of its neighbors’ pulse numbers. This rule stabilizes in time bounded by t?te diameter of the network, it does not revoke global operations, and does not require any additional memory space. However, this rule works correctly only if the pulse numbers may grow unfoundedly. The second part of the construction (whzch is of independent interest in its own right) takes care of this problem. Specifically, we present the jirst self-stabilizing reset procedure that stabilizes in tzme proportional to the diameter of the network. This procedure can be combined with unbounded-register protocols to yield bounded-register algorithms. “Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86K-01 71, NSF contract CCR861 1442, DARPA contract NOOO1489-J-1988, and a special grant from IBM. t IBM T.J. Watson Research Center. $Tel-Aviv University and IBM T.J. Watson Research Center. $Lab. for Computer Science, MIT. Research partly done while visiting IBM T.J. Watson Research Center. Supported in part by DARPA contracts NOOO1 4-92J-4o33 and NOOO1492-J-1799, ONR contract NOOO14-91-J-1O46, and NSF contract 8915206-CCR. !IDEG, 55o King Street, Llttleton, MA 01460. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice ia given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ J993 AG~ Q-89~9J-59 J-7/93 /QQQ51Q652,.. $J.~Q","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129459332","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}
. In this paper we consider the di(cid:14)culty of factoring multivariate polynomials F(x; y;z;:::) modulo n. We consider in particular the case in which F is a product of two randomly chosen polynomials P and Q with algebraically speci(cid:12)ed coe(cid:14)cients, and n is the product of two randomly chosen primes p and q. The general problem of factoring F is known to be at least as hard as the factorization of n, but in many restricted cases (when P or Q are known to have a particular form) the problem can be much easier. The main result of this paper is that (with one trivial exception), the problem of factoring F is at least as hard as the factorization of n whenever P and Q are randomly chosen from the same sample space, regardless of what may be known about its form.
{"title":"On the generation of multivariate polynomials which are hard to factor","authors":"A. Shamir","doi":"10.1145/167088.167291","DOIUrl":"https://doi.org/10.1145/167088.167291","url":null,"abstract":". In this paper we consider the di(cid:14)culty of factoring multivariate polynomials F(x; y;z;:::) modulo n. We consider in particular the case in which F is a product of two randomly chosen polynomials P and Q with algebraically speci(cid:12)ed coe(cid:14)cients, and n is the product of two randomly chosen primes p and q. The general problem of factoring F is known to be at least as hard as the factorization of n, but in many restricted cases (when P or Q are known to have a particular form) the problem can be much easier. The main result of this paper is that (with one trivial exception), the problem of factoring F is at least as hard as the factorization of n whenever P and Q are randomly chosen from the same sample space, regardless of what may be known about its form.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129634430","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}
In this paper we study the ability of array-based networks to tolerate faults. We show that an N x N twodimensional array can sustain N1 -‘ worst-case faults, for any fixed c >0, and still emulate a fully functioning N x N array with only constant slowdown. We also observe that even if every node fails with some fixed probability, p, with high probability the array can still emulate a fully functioning array with constant slowdown. Previously, no connected bounded-degree network was known to be able to tolerate constantprobability node failures without suffering more than a constant-factor loss in performance. Finally, we observe that if faulty nodes are allowed to communicate, but not compute, then an N-node one-dimensional array can tolerate logO(lJ N worst-case faults and still emulate a fault-free array with constant slowdown, and this bound is tight.
本文研究了基于阵列的网络容错能力。我们表明，对于任何固定的c >0, N x N二维数组可以承受N1 - '最坏情况故障，并且仍然可以模拟一个完全功能的N x N数组，只有恒定的减速。我们还观察到，即使每个节点都以固定的概率p失败，在高概率下，数组仍然可以模拟一个具有恒定减速的完整功能的数组。以前，已知没有连接的有界度网络能够容忍恒定概率的节点故障而不遭受超过恒定因素的性能损失。最后，我们观察到，如果允许故障节点进行通信，但不允许进行计算，那么N节点一维数组可以容忍logO(lJ) N个最坏情况故障，并且仍然可以模拟具有恒定减速的无故障数组，并且这个界限很紧。
{"title":"Multi-scale self-simulation: a technique for reconfiguring arrays with faults","authors":"R. Cole, B. Maggs, R. Sitaraman","doi":"10.1145/167088.167235","DOIUrl":"https://doi.org/10.1145/167088.167235","url":null,"abstract":"In this paper we study the ability of array-based networks to tolerate faults. We show that an N x N twodimensional array can sustain N1 -‘ worst-case faults, for any fixed c >0, and still emulate a fully functioning N x N array with only constant slowdown. We also observe that even if every node fails with some fixed probability, p, with high probability the array can still emulate a fully functioning array with constant slowdown. Previously, no connected bounded-degree network was known to be able to tolerate constantprobability node failures without suffering more than a constant-factor loss in performance. Finally, we observe that if faulty nodes are allowed to communicate, but not compute, then an N-node one-dimensional array can tolerate logO(lJ N worst-case faults and still emulate a fault-free array with constant slowdown, and this bound is tight.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"189 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122182880","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":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","authors":"Rao Kosaraju, M. Fellows, A. Wigderson, J. Ellis","doi":"10.1145/129712","DOIUrl":"https://doi.org/10.1145/129712","url":null,"abstract":"","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131134706","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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