Pub Date : 2001-10-14DOI: 10.1109/SFCS.2001.959897
Jittat Fakcharoenphol, Satish Rao
The authors present an O(n log/sup 3/ n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by R. Lipton et al., (1978 )which ran in O(n/sup 3/2/) time, and the best polynomial algorithm developed by M. Henzinger et al. (1994) which ran in O/spl tilde/(n/sup 4/3/) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.
{"title":"Planar graphs, negative weight edges, shortest paths, and near linear time","authors":"Jittat Fakcharoenphol, Satish Rao","doi":"10.1109/SFCS.2001.959897","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959897","url":null,"abstract":"The authors present an O(n log/sup 3/ n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by R. Lipton et al., (1978 )which ran in O(n/sup 3/2/) time, and the best polynomial algorithm developed by M. Henzinger et al. (1994) which ran in O/spl tilde/(n/sup 4/3/) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125521029","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959877
C. Papadimitriou
There has been recently increasing interaction between game theory and, more generally, economic theory, with theoretical computer science, mainly in the context of the Internet. The paper is an invitation to this important frontier.
{"title":"Game theory and mathematical economics: a theoretical computer scientist's introduction","authors":"C. Papadimitriou","doi":"10.1109/SFCS.2001.959877","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959877","url":null,"abstract":"There has been recently increasing interaction between game theory and, more generally, economic theory, with theoretical computer science, mainly in the context of the Internet. The paper is an invitation to this important frontier.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129554095","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959886
B. Barak, Oded Goldreich, S. Goldwasser, Yehuda Lindell
Resettably-sound proofs and arguments maintain soundness even when the prover can reset the verifier to use the same random coins in repeated executions of the protocol. We show that resettably-sound zero-knowledge arguments for NP exist if collision-free hash functions exist. In contrast, resettably-sound zero-knowledge proofs are possible only for languages in P/poly. We present two applications of resettably-sound zero-knowledge arguments. First, we construct resettable zero-knowledge arguments of knowledge for NP, using a natural relaxation of the definition of arguments (and proofs) of knowledge. We note that, under the standard definition of proof of knowledge, it is impossible to obtain resettable zero-knowledge arguments of knowledge for languages outside BPP. Second, we construct a constant-round resettable zero-knowledge argument for NP in the public-key model, under the assumption that collision-free hash functions exist. This improves upon the sub-exponential hardness assumption required by previous constructions. We emphasize that our results use non-black-box zero-knowledge simulations. Indeed, we show that some of the results are impossible to achieve using black-box simulations. In particular, only languages in BPP have resettably-sound arguments that are zero-knowledge with respect to black-box simulation.
{"title":"Resettably-sound zero-knowledge and its applications","authors":"B. Barak, Oded Goldreich, S. Goldwasser, Yehuda Lindell","doi":"10.1109/SFCS.2001.959886","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959886","url":null,"abstract":"Resettably-sound proofs and arguments maintain soundness even when the prover can reset the verifier to use the same random coins in repeated executions of the protocol. We show that resettably-sound zero-knowledge arguments for NP exist if collision-free hash functions exist. In contrast, resettably-sound zero-knowledge proofs are possible only for languages in P/poly. We present two applications of resettably-sound zero-knowledge arguments. First, we construct resettable zero-knowledge arguments of knowledge for NP, using a natural relaxation of the definition of arguments (and proofs) of knowledge. We note that, under the standard definition of proof of knowledge, it is impossible to obtain resettable zero-knowledge arguments of knowledge for languages outside BPP. Second, we construct a constant-round resettable zero-knowledge argument for NP in the public-key model, under the assumption that collision-free hash functions exist. This improves upon the sub-exponential hardness assumption required by previous constructions. We emphasize that our results use non-black-box zero-knowledge simulations. Indeed, we show that some of the results are impossible to achieve using black-box simulations. In particular, only languages in BPP have resettably-sound arguments that are zero-knowledge with respect to black-box simulation.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131640662","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959932
T. Bohman, A. Frieze
Given a digraph D=(V, A) and a set of /spl kappa/ pairs of vertices in V, we are interested in finding for each pair (x/sub i/, y/sub i/), a directed path connecting x/sub i/ to y/sub i/, such that the set of /spl kappa/ paths so found is arc-disjoint. For arbitrary graphs, the problem is /spl Nscr//spl Pscr/-complete, even for /spl kappa/=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of /spl kappa/=/spl Omega/(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.
{"title":"Arc-disjoint paths in expander digraphs","authors":"T. Bohman, A. Frieze","doi":"10.1109/SFCS.2001.959932","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959932","url":null,"abstract":"Given a digraph D=(V, A) and a set of /spl kappa/ pairs of vertices in V, we are interested in finding for each pair (x/sub i/, y/sub i/), a directed path connecting x/sub i/ to y/sub i/, such that the set of /spl kappa/ paths so found is arc-disjoint. For arbitrary graphs, the problem is /spl Nscr//spl Pscr/-complete, even for /spl kappa/=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of /spl kappa/=/spl Omega/(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128672780","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959905
Jin-Yi Cai
We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. We assume that there is an efficient algorithm which can approximately solve a random instance of CVP, with a non-trivial success probability. For lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (including a version of CVP) efficiently for every lattice with high probability.
{"title":"On the average-case hardness of CVP","authors":"Jin-Yi Cai","doi":"10.1109/SFCS.2001.959905","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959905","url":null,"abstract":"We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. We assume that there is an efficient algorithm which can approximately solve a random instance of CVP, with a non-trivial success probability. For lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (including a version of CVP) efficiently for every lattice with high probability.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122064871","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959922
Oded Goldreich, L. Trevisan
Property testing is a relaxation of decision problems in which it is required to distinguish YES-instances (i.e., objects having a predetermined property) from instances that are far from any YES-instance. We present three theorems regarding testing graph properties in the adjacency matrix representation. More specifically, these theorems relate to the project of characterizing graph properties according to the complexity of testing them (in the adjacency matrix representation). The first theorem is that there exist monotone graph properties in /spl Nscr//spl Pscr/ for which testing is very hard (i.e., requires one to examine a constant fraction of the entries in the matrix). The second theorem is that every graph property that can be tested making a number of queries that is independent of the size of the graph, can be so tested by uniformly selecting a set of vertices and accepting iff the induced subgraph has some fixed graph property (which is not necessarily the same as the one being tested). The third theorem refers to the framework of graph partition problems, and is a characterization of the subclass of properties that can be tested using a one-sided error tester, making a number of queries that is independent of the size of the graph.
{"title":"Three theorems regarding testing graph properties","authors":"Oded Goldreich, L. Trevisan","doi":"10.1109/SFCS.2001.959922","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959922","url":null,"abstract":"Property testing is a relaxation of decision problems in which it is required to distinguish YES-instances (i.e., objects having a predetermined property) from instances that are far from any YES-instance. We present three theorems regarding testing graph properties in the adjacency matrix representation. More specifically, these theorems relate to the project of characterizing graph properties according to the complexity of testing them (in the adjacency matrix representation). The first theorem is that there exist monotone graph properties in /spl Nscr//spl Pscr/ for which testing is very hard (i.e., requires one to examine a constant fraction of the entries in the matrix). The second theorem is that every graph property that can be tested making a number of queries that is independent of the size of the graph, can be so tested by uniformly selecting a set of vertices and accepting iff the induced subgraph has some fixed graph property (which is not necessarily the same as the one being tested). The third theorem refers to the framework of graph partition problems, and is a characterization of the subclass of properties that can be tested using a one-sided error tester, making a number of queries that is independent of the size of the graph.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133929920","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959911
A. Storjohann
A deterministic algorithm for computing the Frobenius canonical-form of a matrix over a field is described. A similarity transformation-matrix is recovered in the same time. The algorithm is nearly optimal, requiring about the same number of field operations as required for matrix multiplication. Previously-known reductions to matrix multiplication are probabilistic.
{"title":"Deterministic computation of the Frobenius form","authors":"A. Storjohann","doi":"10.1109/SFCS.2001.959911","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959911","url":null,"abstract":"A deterministic algorithm for computing the Frobenius canonical-form of a matrix over a field is described. A similarity transformation-matrix is recovered in the same time. The algorithm is nearly optimal, requiring about the same number of field operations as required for matrix multiplication. Previously-known reductions to matrix multiplication are probabilistic.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132997010","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959890
B. Awerbuch, P. Berenbrink, A. Brinkmann, C. Scheideler
In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections and one for flow injections) and show that for the case of a single receiver these algorithms will always ensure that the number of packets or flow in the system is bounded at any time step, even for an injection process that completely saturates the capacities of the available edges and even if the network topology changes in a completely unpredictable way. We also show that the maximum number of packets or flow that can be in the system at any time is essentially best possible by providing a lower bound that holds for any online algorithm, whether distributed or not. Interestingly, our balancing algorithms do not behave well in a completely adversarial setting. We show that also in the other extreme of a static network and a static injection pattern the algorithms will converge to a point in which they achieve an average routing time that is close to the best possible average routing time that can be achieved by any strategy. This demonstrates that there are simple algorithms that can be efficient for very different scenarios.
{"title":"Simple routing strategies for adversarial systems","authors":"B. Awerbuch, P. Berenbrink, A. Brinkmann, C. Scheideler","doi":"10.1109/SFCS.2001.959890","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959890","url":null,"abstract":"In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections and one for flow injections) and show that for the case of a single receiver these algorithms will always ensure that the number of packets or flow in the system is bounded at any time step, even for an injection process that completely saturates the capacities of the available edges and even if the network topology changes in a completely unpredictable way. We also show that the maximum number of packets or flow that can be in the system at any time is essentially best possible by providing a lower bound that holds for any online algorithm, whether distributed or not. Interestingly, our balancing algorithms do not behave well in a completely adversarial setting. We show that also in the other extreme of a static network and a static injection pattern the algorithms will converge to a point in which they achieve an average routing time that is close to the best possible average routing time that can be achieved by any strategy. This demonstrates that there are simple algorithms that can be efficient for very different scenarios.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129629199","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959917
A. Meyerson
We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)-competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constant-competitive, and provide an O(log n)-competitive algorithm. Our algorithms are randomized and the analysis depends heavily on the concept of expected waiting time. We also combine our techniques with those of M. Charikar and S. Guha (1999) to provide a linear-time constant approximation for the offline facility location problem.
{"title":"Online facility location","authors":"A. Meyerson","doi":"10.1109/SFCS.2001.959917","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959917","url":null,"abstract":"We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)-competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constant-competitive, and provide an O(log n)-competitive algorithm. Our algorithms are randomized and the analysis depends heavily on the concept of expected waiting time. We also combine our techniques with those of M. Charikar and S. Guha (1999) to provide a linear-time constant approximation for the offline facility location problem.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133397419","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 : 2001-10-14DOI: 10.1109/SFCS.2001.959894
R. Impagliazzo, Nathan Segerlind
We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.
{"title":"Counting axioms do not polynomially simulate counting gates","authors":"R. Impagliazzo, Nathan Segerlind","doi":"10.1109/SFCS.2001.959894","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959894","url":null,"abstract":"We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128785276","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：