The authors consider a situation in which two processors P/sub 1/ and P/sub 2/ are to evaluate one or more functions f/sub 1/, . . ., f/sub s/ of two vector variables x and y, under the assumption that processor P/sub 1/ (respectively, P/sub 2/) has access only to the value of x (respectively, y) and the functional form of f/sub 1/, . . ., f/sub s/. They consider a continuous model of communication whereby real-valued messages are transmitted, and they study the minimum number of messages required for the desired computation. Tight lower bounds are established for the following three problems: (1) each f/sub i/ is a rational function and only one-way communication is allowed. (2) The variables x and y are matrices and the processors wish to solve the linear system (x+y)z=b for the unknown z. (3) The processors wish to evaluate a particular root of the polynomial equation Sigma (x/sub i/+y/sub i/)z/sup i/=0, where the sum is from i=0 to n-1.<>
{"title":"Communication complexity of algebraic computation","authors":"Z. Luo, J. Tsitsiklis","doi":"10.1109/FSCS.1990.89598","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89598","url":null,"abstract":"The authors consider a situation in which two processors P/sub 1/ and P/sub 2/ are to evaluate one or more functions f/sub 1/, . . ., f/sub s/ of two vector variables x and y, under the assumption that processor P/sub 1/ (respectively, P/sub 2/) has access only to the value of x (respectively, y) and the functional form of f/sub 1/, . . ., f/sub s/. They consider a continuous model of communication whereby real-valued messages are transmitted, and they study the minimum number of messages required for the desired computation. Tight lower bounds are established for the following three problems: (1) each f/sub i/ is a rational function and only one-way communication is allowed. (2) The variables x and y are matrices and the processors wish to solve the linear system (x+y)z=b for the unknown z. (3) The processors wish to evaluate a particular root of the polynomial equation Sigma (x/sub i/+y/sub i/)z/sup i/=0, where the sum is from i=0 to n-1.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121906644","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}
A collection of clustering and decomposition techniques that make possible the construction of sparse and locality-preserving representations for arbitrary networks is presented. The representation method considered is based on breaking the network G(V,E) into connected regions, or clusters, thus obtaining a cover for the network, i.e. a collection of clusters that covers the entire set of vertices V. Several other graph-theoretic structures that are strongly related to covers are discussed. These include sparse spanners, tree covers of graphs and the concepts of regional matchings and diameter-based separators. All of these structures can be constructed by means of one of the clustering algorithms given, and each has proved a convenient representation for handling certain network applications.<>
{"title":"Sparse partitions","authors":"B. Awerbuch, David Peleg","doi":"10.1109/FSCS.1990.89571","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89571","url":null,"abstract":"A collection of clustering and decomposition techniques that make possible the construction of sparse and locality-preserving representations for arbitrary networks is presented. The representation method considered is based on breaking the network G(V,E) into connected regions, or clusters, thus obtaining a cover for the network, i.e. a collection of clusters that covers the entire set of vertices V. Several other graph-theoretic structures that are strongly related to covers are discussed. These include sparse spanners, tree covers of graphs and the concepts of regional matchings and diameter-based separators. All of these structures can be constructed by means of one of the clustering algorithms given, and each has proved a convenient representation for handling certain network applications.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124917915","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}
Deterministic competitive k-server algorithms are given for all k and all metric spaces. This settles the k-server conjecture of M.S. Manasse et al. (1988) up to the competitive ratio. The best previous result for general metric spaces was a three-server randomized competitive algorithm and a nonconstructive proof that a deterministic three-server competitive algorithm exists. The competitive ratio the present authors can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open. The methods set forth here also give competitive algorithms for a natural generalization of the k-server problem, called the k-taxicab problem.<>
{"title":"Competitive k-server algorithms","authors":"A. Fiat, Y. Rabani, Yiftach Ravid","doi":"10.1109/FSCS.1990.89566","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89566","url":null,"abstract":"Deterministic competitive k-server algorithms are given for all k and all metric spaces. This settles the k-server conjecture of M.S. Manasse et al. (1988) up to the competitive ratio. The best previous result for general metric spaces was a three-server randomized competitive algorithm and a nonconstructive proof that a deterministic three-server competitive algorithm exists. The competitive ratio the present authors can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open. The methods set forth here also give competitive algorithms for a natural generalization of the k-server problem, called the k-taxicab problem.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130287998","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}
Oded Goldreich, R. Impagliazzo, L. Levin, R. Venkatesan, David Zuckerman
The task of transforming a weak one-way function (which may be easily inverted on all but a polynomial fraction of the range) into a strong one-way function (which can be easily inverted only on a negligible function of the range) is considered. The previously known transformation does not preserve the security (i.e. the running time of the inverting algorithm) within any polynomial. Its resulting function, F(x), applies the weak one-way function to many small (of length mod x mod /sup theta /, theta <1) pieces of the input. Consequently, the function can be inverted for reasonable input lengths by exhaustive search. Random walks on constructive expanders are used to transform any regular (e.g. one-to-one) weak one-way function into a strong one, while preserving security. The resulting function, F(x), applies the weak one-way f to strings of length Theta ( mod x mod ). The security-preserving constructions yield efficient pseudorandom generators and signatures based on any regular one-way function.<>
{"title":"Security preserving amplification of hardness","authors":"Oded Goldreich, R. Impagliazzo, L. Levin, R. Venkatesan, David Zuckerman","doi":"10.1109/FSCS.1990.89550","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89550","url":null,"abstract":"The task of transforming a weak one-way function (which may be easily inverted on all but a polynomial fraction of the range) into a strong one-way function (which can be easily inverted only on a negligible function of the range) is considered. The previously known transformation does not preserve the security (i.e. the running time of the inverting algorithm) within any polynomial. Its resulting function, F(x), applies the weak one-way function to many small (of length mod x mod /sup theta /, theta <1) pieces of the input. Consequently, the function can be inverted for reasonable input lengths by exhaustive search. Random walks on constructive expanders are used to transform any regular (e.g. one-to-one) weak one-way function into a strong one, while preserving security. The resulting function, F(x), applies the weak one-way f to strings of length Theta ( mod x mod ). The security-preserving constructions yield efficient pseudorandom generators and signatures based on any regular one-way function.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122480666","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}
Two of the most commonly used models in computational learning theory are the distribution-free model, in which examples are chosen from a fixed but arbitrary distribution, and the absolute mistake-bound model, in which examples are presented in order by an adversary. Over the Boolean domain
{"title":"Separating distribution-free and mistake-bound learning models over the Boolean domain","authors":"Avrim Blum","doi":"10.1109/FSCS.1990.89540","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89540","url":null,"abstract":"Two of the most commonly used models in computational learning theory are the distribution-free model, in which examples are chosen from a fixed but arbitrary distribution, and the absolute mistake-bound model, in which examples are presented in order by an adversary. Over the Boolean domain","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"353 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122789716","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}
Directed, strongly connected networks of finite-state automata, of bounded in- and outdegree but unknown topology and unbounded size n, are considered. Protocols that are quadratic or linear in n and accomplish the following tasks are provided: waking up and reporting when done, constructing smart spanning trees out from the root and in to the root, conducting breadth-first and depth-first searches, sending a message from the endpoint of a (directed) edge to its startpoint, running a slow clock, and solving the firing squad synchronization problem. The protocols are highly parallel and entail the use of sequences of signals called 'snakes''. All the tasks are accomplished in less time than is possible with any previously known techniques.<>
{"title":"Computing with snakes in directed networks of automata","authors":"S. Even, A. Litman, P. Winkler","doi":"10.1109/FSCS.1990.89596","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89596","url":null,"abstract":"Directed, strongly connected networks of finite-state automata, of bounded in- and outdegree but unknown topology and unbounded size n, are considered. Protocols that are quadratic or linear in n and accomplish the following tasks are provided: waking up and reporting when done, constructing smart spanning trees out from the root and in to the root, conducting breadth-first and depth-first searches, sending a message from the endpoint of a (directed) edge to its startpoint, running a slow clock, and solving the firing squad synchronization problem. The protocols are highly parallel and entail the use of sequences of signals called 'snakes''. All the tasks are accomplished in less time than is possible with any previously known techniques.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122843384","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}
Presents an efficient distributed online algorithm for scheduling jobs that are created dynamically, subject to resource constraints that require that certain pairs of jobs not run concurrently. The focus is on the response time of the system to each job, i.e. the length of the time interval that starts when the job is created or assigned to a processor and ends at the instant the execution of the job begins. The goal is to provide guarantees on the response time to each job j in terms of the density of arrivals of jobs that conflict with j. The model is completely asynchronous and includes various resource allocation problems that have been studied extensively, including the dining philosophers problem and its generalizations to arbitrary networks. In these versions of the problem, the resource requirements of each new job j determines an upper bound delta /sub j/ on the number of jobs that can exist concurrently in the system and conflict with j. Given such upper bounds, no scheduling algorithm can guarantee a response time better than delta /sub j/ times the maximum execution or message transmission time. A simple algorithm that guarantees response time that is essentially polynomial in delta /sub j/ is presented. It is based on the notion of a distribution queue and has a compact implementation.<>
{"title":"A dining philosophers algorithm with polynomial response time","authors":"B. Awerbuch, M. Saks","doi":"10.1109/FSCS.1990.89525","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89525","url":null,"abstract":"Presents an efficient distributed online algorithm for scheduling jobs that are created dynamically, subject to resource constraints that require that certain pairs of jobs not run concurrently. The focus is on the response time of the system to each job, i.e. the length of the time interval that starts when the job is created or assigned to a processor and ends at the instant the execution of the job begins. The goal is to provide guarantees on the response time to each job j in terms of the density of arrivals of jobs that conflict with j. The model is completely asynchronous and includes various resource allocation problems that have been studied extensively, including the dining philosophers problem and its generalizations to arbitrary networks. In these versions of the problem, the resource requirements of each new job j determines an upper bound delta /sub j/ on the number of jobs that can exist concurrently in the system and conflict with j. Given such upper bounds, no scheduling algorithm can guarantee a response time better than delta /sub j/ times the maximum execution or message transmission time. A simple algorithm that guarantees response time that is essentially polynomial in delta /sub j/ is presented. It is based on the notion of a distribution queue and has a compact implementation.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130022277","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}
The author investigates the question of whether or not a specific Boolean function in n variables can be interpolated by an analytic function in the same variables whose partial derivatives of all orders span a subspace of low dimension in the space of analytic functions. The upper and lower bounds for this dimension yield some weak circuit lower bounds. For a particular function, an Omega (n/log n)-size lower bound is obtained for its computation by a circuit whose gates are symmetric. For the same function an Omega (n) lower bound is obtained for the circuit with mod/sub k/ gates.<>
{"title":"On interpolation by analytic functions with special properties and some weak lower bounds on the size of circuits with symmetric gates","authors":"R. Smolensky","doi":"10.1109/FSCS.1990.89584","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89584","url":null,"abstract":"The author investigates the question of whether or not a specific Boolean function in n variables can be interpolated by an analytic function in the same variables whose partial derivatives of all orders span a subspace of low dimension in the space of analytic functions. The upper and lower bounds for this dimension yield some weak circuit lower bounds. For a particular function, an Omega (n/log n)-size lower bound is obtained for its computation by a circuit whose gates are symmetric. For the same function an Omega (n) lower bound is obtained for the circuit with mod/sub k/ gates.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116470274","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}
A point location scheme is presented for an n-vertex dynamic planar subdivision whose underlying graph is only required to be connected. The scheme uses O(n) space and yields an O(log/sup 2/n) query time and an O(log n) update time. Insertion (respectively, deletion) of an arbitrary k-edge chain inside a region can be performed in O(k log(n+k)) (respectively, O(k log n)) time. The scheme is then extended to speed up the insertion/deletion of a k-edge monotone chain to O(log/sup 2/n log log n+k) time (or O(log n log log n+k) time for an alternative model of input), but at the expense of increasing the other time bounds slightly. All bounds are worst case. Additional results include a generalization to planar subdivisions consisting of algebraic segments of bounded degree and a persistent scheme for planar point location.<>
{"title":"New results on dynamic planar point location","authors":"Siu-Wing Cheng, Ravi Janardan","doi":"10.1109/FSCS.1990.89528","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89528","url":null,"abstract":"A point location scheme is presented for an n-vertex dynamic planar subdivision whose underlying graph is only required to be connected. The scheme uses O(n) space and yields an O(log/sup 2/n) query time and an O(log n) update time. Insertion (respectively, deletion) of an arbitrary k-edge chain inside a region can be performed in O(k log(n+k)) (respectively, O(k log n)) time. The scheme is then extended to speed up the insertion/deletion of a k-edge monotone chain to O(log/sup 2/n log log n+k) time (or O(log n log log n+k) time for an alternative model of input), but at the expense of increasing the other time bounds slightly. All bounds are worst case. Additional results include a generalization to planar subdivisions consisting of algebraic segments of bounded degree and a persistent scheme for planar point location.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116006905","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}
It is shown that randomization helps in coloring graphs online, and a simple randomized online algorithm is presented. For 3-colorable graphs the expected number of colors the algorithm uses is O((n log n)/sup 1/2/). The algorithm runs in polynomial time and compares well with the best known polynomial-time offline algorithms. A lower bound is proved for the randomized algorithm.<>
{"title":"Randomized online graph coloring","authors":"S. Vishwanathan","doi":"10.1109/FSCS.1990.89567","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89567","url":null,"abstract":"It is shown that randomization helps in coloring graphs online, and a simple randomized online algorithm is presented. For 3-colorable graphs the expected number of colors the algorithm uses is O((n log n)/sup 1/2/). The algorithm runs in polynomial time and compares well with the best known polynomial-time offline algorithms. A lower bound is proved for the randomized algorithm.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125716092","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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