Pub Date : 2001-10-14DOI: 10.1109/SFCS.2001.959880
V. Koltun
We show that the complexity of the vertical decomposition of an arrangement of n fixed-degree algebraic surfaces or surface patches in four dimensions is O(n/sup 4+/spl epsi//) for any /spl epsi/ > 0. This improves the best previously known upper bound for this problem by a near-linear factor, and settles a major problem in the theory of arrangements of surfaces, open since 1989. The new bound can be extended to higher dimensions, yielding the bound O (n/sup 2d-4+/spl epsi//), for any /spl epsi/ > 0, on the complexity of vertical decompositions in dimensions d /spl ges/ 4. We also describe the immediate algorithmic applications of these results, which include improved algorithms for point location, range searching, ray shooting, robot motion planning, and some geometric optimization problems.
{"title":"Almost tight upper bounds for vertical decompositions in four dimensions","authors":"V. Koltun","doi":"10.1109/SFCS.2001.959880","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959880","url":null,"abstract":"We show that the complexity of the vertical decomposition of an arrangement of n fixed-degree algebraic surfaces or surface patches in four dimensions is O(n/sup 4+/spl epsi//) for any /spl epsi/ > 0. This improves the best previously known upper bound for this problem by a near-linear factor, and settles a major problem in the theory of arrangements of surfaces, open since 1989. The new bound can be extended to higher dimensions, yielding the bound O (n/sup 2d-4+/spl epsi//), for any /spl epsi/ > 0, on the complexity of vertical decompositions in dimensions d /spl ges/ 4. We also describe the immediate algorithmic applications of these results, which include improved algorithms for point location, range searching, ray shooting, robot motion planning, and some geometric optimization 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":"114996051","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.2001.959878
P. Indyk
The author surveys algorithmic results obtained using low-distortion embeddings of metric spaces into (mostly) normed spaces. He shows that low-distortion embeddings provide a powerful and versatile toolkit for solving algorithmic problems. Their fundamental nature makes them applicable in a variety of diverse settings, while their relation to rich mathematical fields (e.g., functional analysis) ensures availability of tools for their construction.
{"title":"Algorithmic applications of low-distortion geometric embeddings","authors":"P. Indyk","doi":"10.1109/SFCS.2001.959878","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959878","url":null,"abstract":"The author surveys algorithmic results obtained using low-distortion embeddings of metric spaces into (mostly) normed spaces. He shows that low-distortion embeddings provide a powerful and versatile toolkit for solving algorithmic problems. Their fundamental nature makes them applicable in a variety of diverse settings, while their relation to rich mathematical fields (e.g., functional analysis) ensures availability of tools for their construction.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"50 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":"121553110","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 : 2001-10-08DOI: 10.1109/SFCS.2001.959902
W. V. Dam, M. Mosca, U. Vazirani
The authors analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'. Adiabatic quantum computation is a novel paradigm for the design of quantum algorithms; it is truly quantum in the sense that it can be used to speed up searching by a quadratic factor over any classical algorithm. On the question of whether this new paradigm may be used to efficiently solve NP-complete problems on a quantum computer, we show that the usual query complexity arguments cannot be used to rule out a polynomial time solution. On the other hand, we argue that the adiabatic approach may be thought of as a kind of 'quantum local search'. We design a family of minimization problems that is hard for such local search heuristics, and establish an exponential lower bound for the adiabatic algorithm for these problems. This provides insights into the limitations of this approach. It remains an open question whether adiabatic quantum computation can establish an exponential speed-up over traditional computing or if there exists a classical algorithm that can simulate the quantum adiabatic process efficiently.
{"title":"How powerful is adiabatic quantum computation?","authors":"W. V. Dam, M. Mosca, U. Vazirani","doi":"10.1109/SFCS.2001.959902","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959902","url":null,"abstract":"The authors analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'. Adiabatic quantum computation is a novel paradigm for the design of quantum algorithms; it is truly quantum in the sense that it can be used to speed up searching by a quadratic factor over any classical algorithm. On the question of whether this new paradigm may be used to efficiently solve NP-complete problems on a quantum computer, we show that the usual query complexity arguments cannot be used to rule out a polynomial time solution. On the other hand, we argue that the adiabatic approach may be thought of as a kind of 'quantum local search'. We design a family of minimization problems that is hard for such local search heuristics, and establish an exponential lower bound for the adiabatic algorithm for these problems. This provides insights into the limitations of this approach. It remains an open question whether adiabatic quantum computation can establish an exponential speed-up over traditional computing or if there exists a classical algorithm that can simulate the quantum adiabatic process efficiently.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132165585","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 : 2001-10-08DOI: 10.1109/SFCS.2001.959879
M. Sudan
Coding theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of coding theory. More recently, theoretical computer science has also been contributing to the theory of error-correcting codes in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of coding theory and the progress made via algebraic methods. We stress that this is a very partial view of coding theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey.
{"title":"Coding theory: tutorial & survey","authors":"M. Sudan","doi":"10.1109/SFCS.2001.959879","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959879","url":null,"abstract":"Coding theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of coding theory. More recently, theoretical computer science has also been contributing to the theory of error-correcting codes in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of coding theory and the progress made via algebraic methods. We stress that this is a very partial view of coding theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"141 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123424639","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 : 2001-10-08DOI: 10.1109/SFCS.2001.959938
Jin-Yi Cai
We show that the class Sp2 is a subclass of ZPP . The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPP .
{"title":"S/sub 2/ ZPP/sup NP/","authors":"Jin-Yi Cai","doi":"10.1109/SFCS.2001.959938","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959938","url":null,"abstract":"We show that the class Sp2 is a subclass of ZPP . The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPP .","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128105385","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 : 2001-10-08DOI: 10.1109/SFCS.2001.959927
W. Aiello, F. Graham, Linyuan Lu
Many massive graphs (such as the WWW graph and Call graphs) share certain universal characteristics which can be described by the so-called "power law." In this paper, we, examine three important aspects of power law graphs, (1) the evolution of power law graphs, (2) the asymmetry of in-degrees and out-degrees, (3) the "scale invariance" of power law graphs. In particular, we give three increasingly general directed graph models and one general undirected graph model for generating power law graphs by adding at most one node and possibly one or more edges at a time. We show that for any given edge density and desired power laws for in-degrees and out-degrees, not necessarily the same, the resulting graph will almost surely have the desired edge density and the power laws for the in-degrees and out-degrees. Our most general directed and undirected models include nearly all known power law evolution models as special cases. Finally, we show that our evolution models generate "scale invariant" graphs. We describe a method for scaling the time in our evolution model such that the power law of the degree sequences remains invariant.
{"title":"Random evolution in massive graphs","authors":"W. Aiello, F. Graham, Linyuan Lu","doi":"10.1109/SFCS.2001.959927","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959927","url":null,"abstract":"Many massive graphs (such as the WWW graph and Call graphs) share certain universal characteristics which can be described by the so-called \"power law.\" In this paper, we, examine three important aspects of power law graphs, (1) the evolution of power law graphs, (2) the asymmetry of in-degrees and out-degrees, (3) the \"scale invariance\" of power law graphs. In particular, we give three increasingly general directed graph models and one general undirected graph model for generating power law graphs by adding at most one node and possibly one or more edges at a time. We show that for any given edge density and desired power laws for in-degrees and out-degrees, not necessarily the same, the resulting graph will almost surely have the desired edge density and the power laws for the in-degrees and out-degrees. Our most general directed and undirected models include nearly all known power law evolution models as special cases. Finally, we show that our evolution models generate \"scale invariant\" graphs. We describe a method for scaling the time in our evolution model such that the power law of the degree sequences remains invariant.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125624154","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 : 2001-10-08DOI: 10.1109/SFCS.2001.959930
N. Young
We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (aka mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1/spl plusmn//spl epsi/ factor in O(mdlog(m)//spl epsi//sup 2/) time, where m is the number of constraints and d is the maximum number of constraints any variable appears in. Our parallel algorithm runs in time polylogarithmic in the input size times /spl epsi//sup -4/ and uses a total number of operations comparable to the sequential algorithm. The main contribution is that the algorithms solve mixed packing and covering problems (in contrast to pure packing or pure covering problems, which have only "/spl les/" or only "/spl ges/" inequalities, but not both) and run in time independent of the so-called width of the problem.
{"title":"Sequential and parallel algorithms for mixed packing and covering","authors":"N. Young","doi":"10.1109/SFCS.2001.959930","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959930","url":null,"abstract":"We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (aka mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1/spl plusmn//spl epsi/ factor in O(mdlog(m)//spl epsi//sup 2/) time, where m is the number of constraints and d is the maximum number of constraints any variable appears in. Our parallel algorithm runs in time polylogarithmic in the input size times /spl epsi//sup -4/ and uses a total number of operations comparable to the sequential algorithm. The main contribution is that the algorithms solve mixed packing and covering problems (in contrast to pure packing or pure covering problems, which have only \"/spl les/\" or only \"/spl ges/\" inequalities, but not both) and run in time independent of the so-called width of the problem.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122444739","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 : 2001-08-18DOI: 10.1109/SFCS.2001.959926
D. Achlioptas, A. Fiat, Anna R. Karlin, Frank McSherry
We present a model for web search that captures in a unified manner three critical components of the problem: how the link structure of the web is generated, how the content of a web document is generated, and how a human searcher generates a query. The key to this unification lies in capturing the correlations between these components in terms of proximity in a shared latent semantic space. Given such a combined model, the correct answer to a search query is well defined, and thus it becomes possible to evaluate web search algorithms rigorously. We present a new web search algorithm, based on spectral techniques, and prove that it is guaranteed to produce an approximately correct answer in our model. The algorithm assumes no knowledge of the model, and is well-defined regardless of the model's accuracy.
{"title":"Web search via hub synthesis","authors":"D. Achlioptas, A. Fiat, Anna R. Karlin, Frank McSherry","doi":"10.1109/SFCS.2001.959926","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959926","url":null,"abstract":"We present a model for web search that captures in a unified manner three critical components of the problem: how the link structure of the web is generated, how the content of a web document is generated, and how a human searcher generates a query. The key to this unification lies in capturing the correlations between these components in terms of proximity in a shared latent semantic space. Given such a combined model, the correct answer to a search query is well defined, and thus it becomes possible to evaluate web search algorithms rigorously. We present a new web search algorithm, based on spectral techniques, and prove that it is guaranteed to produce an approximately correct answer in our model. The algorithm assumes no knowledge of the model, and is well-defined regardless of the model's accuracy.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"315 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116537817","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 : 2001-06-28DOI: 10.1109/SFCS.2001.959903
H. Klauck
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by R. Raz (1995) to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity and nondeterministic quantum communication complexity. We develop several other Fourier based lower bound methods, notably showing that /spl radic/(s~(f)/log n) n, for the average sensitivity s~(f) of a function f, yields a lower bound on the bounded error quantum communication complexity of f (x/spl and/y/spl oplus/yz), where x is a Boolean word held by Alice and y, z are Boolean words held by Bob. We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible. For all the functions we investigate, only the previously applied general lower bound method based on discrepancy yields bounds that are O(log n).
{"title":"Lower bounds for quantum communication complexity","authors":"H. Klauck","doi":"10.1109/SFCS.2001.959903","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959903","url":null,"abstract":"We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by R. Raz (1995) to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity and nondeterministic quantum communication complexity. We develop several other Fourier based lower bound methods, notably showing that /spl radic/(s~(f)/log n) n, for the average sensitivity s~(f) of a function f, yields a lower bound on the bounded error quantum communication complexity of f (x/spl and/y/spl oplus/yz), where x is a Boolean word held by Alice and y, z are Boolean words held by Bob. We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible. For all the functions we investigate, only the previously applied general lower bound method based on discrepancy yields bounds that are O(log n).","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"414 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122809150","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 : 2001-04-26DOI: 10.1109/SFCS.2001.959892
P. Berenbrink, Tom Friedetzky, L. A. Goldberg
In this paper we analyse a very simple dynamic work-stealing algorithm. In the work-generation model, there are n generators which are arbitrarily distributed among a set of n processors. During each time-step, with probability /spl lambda/, each generator generates a unit-time task which it inserts into the queue of its host processor. After the new tasks are generated, each processor removes one task from its queue and services it. Clearly, the work-generation model allows the load to grow more and more imbalanced, so, even when /spl lambda/<1, the system load can be unbounded. The natural work-stealing algorithm that we analyse works as follows. During each time step, each empty processor sends a request to a randomly selected other processor. Any non-empty processor having received at least one such request in turn decides (again randomly) in favour of one of the requests. The number of tasks which are transferred from the non-empty processor to the empty one is determined by the so-called work-stealing function f. We analyse the long-term behaviour of the system as a function of /spl lambda/ and f. We show that the system is stable for any constant generation rate /spl lambda/<1 and for a wide class of functions f. We give a quantitative description of the functions f which lead to stable systems. Furthermore, we give upper bounds on the average system load (as a function of f and n).
{"title":"The natural work-stealing algorithm is stable","authors":"P. Berenbrink, Tom Friedetzky, L. A. Goldberg","doi":"10.1109/SFCS.2001.959892","DOIUrl":"https://doi.org/10.1109/SFCS.2001.959892","url":null,"abstract":"In this paper we analyse a very simple dynamic work-stealing algorithm. In the work-generation model, there are n generators which are arbitrarily distributed among a set of n processors. During each time-step, with probability /spl lambda/, each generator generates a unit-time task which it inserts into the queue of its host processor. After the new tasks are generated, each processor removes one task from its queue and services it. Clearly, the work-generation model allows the load to grow more and more imbalanced, so, even when /spl lambda/<1, the system load can be unbounded. The natural work-stealing algorithm that we analyse works as follows. During each time step, each empty processor sends a request to a randomly selected other processor. Any non-empty processor having received at least one such request in turn decides (again randomly) in favour of one of the requests. The number of tasks which are transferred from the non-empty processor to the empty one is determined by the so-called work-stealing function f. We analyse the long-term behaviour of the system as a function of /spl lambda/ and f. We show that the system is stable for any constant generation rate /spl lambda/<1 and for a wide class of functions f. We give a quantitative description of the functions f which lead to stable systems. Furthermore, we give upper bounds on the average system load (as a function of f and n).","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123280637","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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