Pub Date : 2001-10-14DOI: 10.1109/SFCS.2001.959925
Gopal Pandurangan, P. Raghavan, E. Upfal
In a peer-to-peer (P2P) network, nodes connect into an existing network and participate in providing and availing of services. There is no dichotomy between a central server and distributed clients. Current P2P networks (e.g., Gnutella) are constructed by participants following their own uncoordinated (and often whimsical) protocols; they consequently suffer from frequent network overload and fragmentation into disconnected pieces separated by choke-points with inadequate bandwidth. The authors propose a simple scheme for participants to build P2P networks in a distributed fashion, and prove that it results in connected networks of constant degree and logarithmic diameter. It does so with no global knowledge of all the nodes in the network. In the most common P2P application to date (search), these properties are important.
{"title":"Building low-diameter P2P networks","authors":"Gopal Pandurangan, P. Raghavan, E. Upfal","doi":"10.1109/SFCS.2001.959925","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959925","url":null,"abstract":"In a peer-to-peer (P2P) network, nodes connect into an existing network and participate in providing and availing of services. There is no dichotomy between a central server and distributed clients. Current P2P networks (e.g., Gnutella) are constructed by participants following their own uncoordinated (and often whimsical) protocols; they consequently suffer from frequent network overload and fragmentation into disconnected pieces separated by choke-points with inadequate bandwidth. The authors propose a simple scheme for participants to build P2P networks in a distributed fashion, and prove that it results in connected networks of constant degree and logarithmic diameter. It does so with no global knowledge of all the nodes in the network. In the most common P2P application to date (search), these properties are important.","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":"115392318","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.2001.959940
A. Ta-Shma, David Zuckerman, S. Safra
Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. Previous research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, was noticed before. Yet, researchers had failed to build extractors directly from a good code without using other tools from pseudorandomness. We succeed in constructing an extractor directly from a Reed-Muller code. To do this, we develop a novel proof technique. Furthermore, our construction is the first to achieve a degree close to linear. In contrast, the best previous constructions brought the log of the degree within a constant of optimal, which gives polynomial degree. This improvement is important for certain applications. For example, it follows that approximating the VC dimension to within a factor of N/sup 1-/spl delta// is AM-hard for any positive /spl delta/.
{"title":"Extractors from Reed-Muller codes","authors":"A. Ta-Shma, David Zuckerman, S. Safra","doi":"10.1109/SFCS.2001.959940","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959940","url":null,"abstract":"Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. Previous research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, was noticed before. Yet, researchers had failed to build extractors directly from a good code without using other tools from pseudorandomness. We succeed in constructing an extractor directly from a Reed-Muller code. To do this, we develop a novel proof technique. Furthermore, our construction is the first to achieve a degree close to linear. In contrast, the best previous constructions brought the log of the degree within a constant of optimal, which gives polynomial degree. This improvement is important for certain applications. For example, it follows that approximating the VC dimension to within a factor of N/sup 1-/spl delta// is AM-hard for any positive /spl delta/.","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":"130826916","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.2001.959920
Tugkan Batu, L. Fortnow, E. Fischer, Ravi Kumar, R. Rubinfeld, Patrick White
Given access to independent samples of a distribution A over [n] /spl times/ [m], we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is /spl epsi/-close in the L/sub 1/ norm to the product distribution A/sub 1//spl times/A/sub 2/ for some distributions A/sub 1/ over [n] and A/sub 2/ over [m]. The sample complexity of our test is O/spl tilde/(n/sup 2/3/m/sup 1/3/poly(/spl epsi//sup -1/)), assuming without loss of generality that m/spl les/n. We also give a matching lower bound, up to poly (log n, /spl epsi//sup -1/) factors. Furthermore, given access to samples of a distribution X over [n], we show how to test if X is /spl epsi/-close in L/sub 1/ norm to an explicitly specified distribution Y. Our test uses O/spl tilde/(n/sup 1/2/poly(/spl epsi//sup -1/)) samples, which nearly matches the known tight bounds for the case when Y is uniform.
{"title":"Testing random variables for independence and identity","authors":"Tugkan Batu, L. Fortnow, E. Fischer, Ravi Kumar, R. Rubinfeld, Patrick White","doi":"10.1109/SFCS.2001.959920","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959920","url":null,"abstract":"Given access to independent samples of a distribution A over [n] /spl times/ [m], we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is /spl epsi/-close in the L/sub 1/ norm to the product distribution A/sub 1//spl times/A/sub 2/ for some distributions A/sub 1/ over [n] and A/sub 2/ over [m]. The sample complexity of our test is O/spl tilde/(n/sup 2/3/m/sup 1/3/poly(/spl epsi//sup -1/)), assuming without loss of generality that m/spl les/n. We also give a matching lower bound, up to poly (log n, /spl epsi//sup -1/) factors. Furthermore, given access to samples of a distribution X over [n], we show how to test if X is /spl epsi/-close in L/sub 1/ norm to an explicitly specified distribution Y. Our test uses O/spl tilde/(n/sup 1/2/poly(/spl epsi//sup -1/)) samples, which nearly matches the known tight bounds for the case when Y is uniform.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"108 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":"121822001","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.2001.959941
Ronen Shaltiel, C. Umans
We present a simple, self-contained extractor construction that produces good extractors for all min-entropies (min-entropy measures the amount of randomness contained in a weak random source). Our construction is algebraic and builds on a new polynomial-based approach introduced by A. Ta-Shma et al. (2001). Using our improvements, we obtain, for example, an extractor with output length m=k/sup 1-/spl delta// and seed length O(log n). This matches the parameters of L. Trevisan's (1999) breakthrough result and additionally achieves those parameters for small min-entropies k. Our construction gives a much simpler and more direct solution to this problem. Applying similar ideas to the problem of building pseudo-random generators, we obtain a new pseudo-random generator construction that is not based on the NW generator (N. Nisan and A. Widgerson, 1994), and turns worst-case hardness directly into pseudo-randomness. The parameters of this generator are strong enough to obtain a new proof that P=BPP if E requires exponential size circuits. Essentially, the same construction yields a hitting set generator with optimal seed length that outputs s/sup /spl Omega/(1)/ bits when given a function that requires circuits of size s (for any s). This implies a hardness versus randomness trade off for RP and BPP that is optimal (up to polynomial factors), solving an open problem raised by R. Impagliazzo et al. (1999). Our generators can also be used to derandomize AM.
{"title":"Simple extractors for all min-entropies and a new pseudo-random generator","authors":"Ronen Shaltiel, C. Umans","doi":"10.1109/SFCS.2001.959941","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959941","url":null,"abstract":"We present a simple, self-contained extractor construction that produces good extractors for all min-entropies (min-entropy measures the amount of randomness contained in a weak random source). Our construction is algebraic and builds on a new polynomial-based approach introduced by A. Ta-Shma et al. (2001). Using our improvements, we obtain, for example, an extractor with output length m=k/sup 1-/spl delta// and seed length O(log n). This matches the parameters of L. Trevisan's (1999) breakthrough result and additionally achieves those parameters for small min-entropies k. Our construction gives a much simpler and more direct solution to this problem. Applying similar ideas to the problem of building pseudo-random generators, we obtain a new pseudo-random generator construction that is not based on the NW generator (N. Nisan and A. Widgerson, 1994), and turns worst-case hardness directly into pseudo-randomness. The parameters of this generator are strong enough to obtain a new proof that P=BPP if E requires exponential size circuits. Essentially, the same construction yields a hitting set generator with optimal seed length that outputs s/sup /spl Omega/(1)/ bits when given a function that requires circuits of size s (for any s). This implies a hardness versus randomness trade off for RP and BPP that is optimal (up to polynomial factors), solving an open problem raised by R. Impagliazzo et al. (1999). Our generators can also be used to derandomize AM.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"75 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":"115235544","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.2001.959887
Yael Gertner, T. Malkin, Omer Reingold
We prove that, somewhat surprisingly, there is no black-box reduction of (poly-to-one) trapdoor functions to trapdoor predicates (equivalently, to public-key encryption schemes). Our proof follows the methodology that was introduced by R. Impagliazzo and S. Rudich (1989), although we use a new, weaker model of separation.
{"title":"On the impossibility of basing trapdoor functions on trapdoor predicates","authors":"Yael Gertner, T. Malkin, Omer Reingold","doi":"10.1109/SFCS.2001.959887","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959887","url":null,"abstract":"We prove that, somewhat surprisingly, there is no black-box reduction of (poly-to-one) trapdoor functions to trapdoor predicates (equivalently, to public-key encryption schemes). Our proof follows the methodology that was introduced by R. Impagliazzo and S. Rudich (1989), although we use a new, weaker model of separation.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"1938 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":"128980890","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.2001.959914
Y. Bartal, B. Bollobás, M. Mendel
The paper gives a nearly logarithmic lower bound on the randomized competitive ratio for a Metrical Task Systems model (A. Borodin et al., 1992). This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. In particular, we prove that in every metric space there exists a large subspace which is approximately a "hierarchically well-separated tree" (HST) (Y. Bartal, 1996). This theorem may be of independent interest.
本文给出了一个测量任务系统模型的随机竞争比的近乎对数的下界(a . Borodin et al.， 1992)。这意味着广泛研究的K-server问题也有类似的下界。我们的证明是基于对度量空间的ramsey型定理的证明。特别地，我们证明了在每个度量空间中存在一个大的子空间，它近似于一个“层次上良好分离的树”(Y. Bartal, 1996)。这个定理可能有独立的意义。
{"title":"A Ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems","authors":"Y. Bartal, B. Bollobás, M. Mendel","doi":"10.1109/SFCS.2001.959914","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959914","url":null,"abstract":"The paper gives a nearly logarithmic lower bound on the randomized competitive ratio for a Metrical Task Systems model (A. Borodin et al., 1992). This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. In particular, we prove that in every metric space there exists a large subspace which is approximately a \"hierarchically well-separated tree\" (HST) (Y. Bartal, 1996). This theorem may be of independent interest.","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":"129146180","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.2001.959918
N. Alon
Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least /spl epsi/n/sup 2/ edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (/spl epsi/, H)n/sup h/ copies of H. We show that the largest possible function f (/spl epsi/, H) is polynomial in /spl epsi/ if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1//spl epsi/, if and only if H is bipartite.
{"title":"Testing subgraphs in large graphs","authors":"N. Alon","doi":"10.1109/SFCS.2001.959918","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959918","url":null,"abstract":"Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least /spl epsi/n/sup 2/ edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (/spl epsi/, H)n/sup h/ copies of H. We show that the largest possible function f (/spl epsi/, H) is polynomial in /spl epsi/ if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1//spl epsi/, if and only if H is bipartite.","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":"115940194","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.2001.959942
V. Guruswami, P. Indyk
We present several novel constructions of codes which share the common thread of using expander (or expander-like) graphs as a component. The expanders enable the design of efficient decoding algorithms that correct a large number of errors through various forms of "voting" procedures. We consider both the notions of unique and list decoding, and in all cases obtain asymptotically good codes which are decodable up to a "maximum" possible radius and either: (a) achieve a similar rate as the previously best known codes but come with significantly faster algorithms, or (b) achieve a rate better than any prior construction with similar error-correction properties. Among our main results are: i) codes of rate /spl Omega/(/spl epsi//sup 2/) over constant-sized alphabet that can be list decoded in quadratic time from (1-/spl epsi/) errors; ii) codes of rate /spl Omega/(/spl epsi/) over constant-sized alphabet that can be uniquely decoded from (1/2-/spl epsi/) errors in near-linear time (this matches AG-codes with much faster algorithms); iii) linear-time encodable and decodable binary codes of positive rate (in fact, rate /spl Omega/(/spl epsi//sup 2/)) that can correct up to (1/4-/spl epsi/) fraction errors.
{"title":"Expander-based constructions of efficiently decodable codes","authors":"V. Guruswami, P. Indyk","doi":"10.1109/SFCS.2001.959942","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959942","url":null,"abstract":"We present several novel constructions of codes which share the common thread of using expander (or expander-like) graphs as a component. The expanders enable the design of efficient decoding algorithms that correct a large number of errors through various forms of \"voting\" procedures. We consider both the notions of unique and list decoding, and in all cases obtain asymptotically good codes which are decodable up to a \"maximum\" possible radius and either: (a) achieve a similar rate as the previously best known codes but come with significantly faster algorithms, or (b) achieve a rate better than any prior construction with similar error-correction properties. Among our main results are: i) codes of rate /spl Omega/(/spl epsi//sup 2/) over constant-sized alphabet that can be list decoded in quadratic time from (1-/spl epsi/) errors; ii) codes of rate /spl Omega/(/spl epsi/) over constant-sized alphabet that can be uniquely decoded from (1/2-/spl epsi/) errors in near-linear time (this matches AG-codes with much faster algorithms); iii) linear-time encodable and decodable binary codes of positive rate (in fact, rate /spl Omega/(/spl epsi//sup 2/)) that can correct up to (1/4-/spl epsi/) fraction errors.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"79 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":"126343179","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.2001.959908
L. Fleischer, K. Jain, David P. Williamson
In the survivable network design problem (SNDP), given an undirected graph and values r/sub ij/ for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are r/sub ij/ disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SNDP), the paths must be vertex disjoint. K. Jain et al. (1999) propose a version of the problem intermediate in difficulty to these two, called the element connectivity problem (ELC-SNDP, or ELC). These variants of SNDP are all known to be NP-hard. The best known approximation algorithm for the EC-SNDP has performance guarantee of 2 (K. Jain, 2001), and iteratively rounds solutions to a linear programming relaxation of the problem. ELC has a primal-dual O (log k) approximation algorithm, where k=max/sub i,j/ r/sub ij/. VC-SNDP is not known to have a non-trivial approximation algorithm; however, recently L. Fleischer (2001) has shown how to extend the technique of K. Jain ( 2001) to give a 2-approximation algorithm in the case that r/sub ij//spl isin/{0, 1, 2}. She also shows that the same techniques will not work for VC-SNDP for more general values of r/sub ij/. The authors show that these techniques can be extended to a 2-approximation algorithm for ELC. This gives the first constant approximation algorithm for a general survivable network design problem which allows node failures.
{"title":"An iterative rounding 2-approximation algorithm for the element connectivity problem","authors":"L. Fleischer, K. Jain, David P. Williamson","doi":"10.1109/SFCS.2001.959908","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959908","url":null,"abstract":"In the survivable network design problem (SNDP), given an undirected graph and values r/sub ij/ for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are r/sub ij/ disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SNDP), the paths must be vertex disjoint. K. Jain et al. (1999) propose a version of the problem intermediate in difficulty to these two, called the element connectivity problem (ELC-SNDP, or ELC). These variants of SNDP are all known to be NP-hard. The best known approximation algorithm for the EC-SNDP has performance guarantee of 2 (K. Jain, 2001), and iteratively rounds solutions to a linear programming relaxation of the problem. ELC has a primal-dual O (log k) approximation algorithm, where k=max/sub i,j/ r/sub ij/. VC-SNDP is not known to have a non-trivial approximation algorithm; however, recently L. Fleischer (2001) has shown how to extend the technique of K. Jain ( 2001) to give a 2-approximation algorithm in the case that r/sub ij//spl isin/{0, 1, 2}. She also shows that the same techniques will not work for VC-SNDP for more general values of r/sub ij/. The authors show that these techniques can be extended to a 2-approximation algorithm for ELC. This gives the first constant approximation algorithm for a general survivable network design problem which allows node failures.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"7 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":"125769322","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.2001.959900
C. Demetrescu, G. Italiano
We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates deterministically in O(S/spl middot/n/sup 2.5/log/sup 3/n) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.
{"title":"Fully dynamic all pairs shortest paths with real edge weights","authors":"C. Demetrescu, G. Italiano","doi":"10.1109/SFCS.2001.959900","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959900","url":null,"abstract":"We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates deterministically in O(S/spl middot/n/sup 2.5/log/sup 3/n) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"141 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":"132011761","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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