Pub Date : 1999-10-17DOI: 10.1109/SFFCS.1999.814587
P. Indyk
The metric 2-clustering problem is defined as follows: given a metric (or weighted graph) (X,d), partition X into two sets S(1) and S(2) in order to minimize the value of /spl Sigma//sub i//spl Sigma//sub {u,v}/spl sub/S(i)/d(u,v). In this paper, we show an approximation scheme for this problem.
{"title":"A sublinear time approximation scheme for clustering in metric spaces","authors":"P. Indyk","doi":"10.1109/SFFCS.1999.814587","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814587","url":null,"abstract":"The metric 2-clustering problem is defined as follows: given a metric (or weighted graph) (X,d), partition X into two sets S(1) and S(2) in order to minimize the value of /spl Sigma//sub i//spl Sigma//sub {u,v}/spl sub/S(i)/d(u,v). In this paper, we show an approximation scheme for this problem.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125413698","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814598
Y. Afek, Gideon Stupp, D. Touitou
A distributed algorithm is adaptive if the worst case step complexity of its operations is bounded by a function of the number of processes that are concurrently active during the operation (rather than a function of N, the total number of processes, which is usually much larger). We present long-lived and adaptive algorithms for collect in the read/write shared-memory model. Replacing the reads and writes in long-lived shared memory algorithms with our adaptive collect results in many cases in a corresponding long-lived algorithm which is adaptive. Examples of such applications, which are discussed are atomic-snapshots, and l-exclusion. Following the long-lived and adaptive collect we present a more pragmatic version of collect, called active set. This algorithm is slightly weaker than the collect but has several advantages. We employ this algorithm to transform algorithms, such as the Bakery algorithm, into their corresponding adaptive long-lived version, which is more efficient than the version that was obtained with the collect. Previously, long-lived and adaptive algorithms in this model were presented only for the renaming problem.
{"title":"Long-lived adaptive collect with applications","authors":"Y. Afek, Gideon Stupp, D. Touitou","doi":"10.1109/SFFCS.1999.814598","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814598","url":null,"abstract":"A distributed algorithm is adaptive if the worst case step complexity of its operations is bounded by a function of the number of processes that are concurrently active during the operation (rather than a function of N, the total number of processes, which is usually much larger). We present long-lived and adaptive algorithms for collect in the read/write shared-memory model. Replacing the reads and writes in long-lived shared memory algorithms with our adaptive collect results in many cases in a corresponding long-lived algorithm which is adaptive. Examples of such applications, which are discussed are atomic-snapshots, and l-exclusion. Following the long-lived and adaptive collect we present a more pragmatic version of collect, called active set. This algorithm is slightly weaker than the collect but has several advantages. We employ this algorithm to transform algorithms, such as the Bakery algorithm, into their corresponding adaptive long-lived version, which is more efficient than the version that was obtained with the collect. Previously, long-lived and adaptive algorithms in this model were presented only for the renaming problem.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125898320","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814627
J. Kim, Daniel R. Simon, P. Tetali
Naor and Yung (1989) show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by /spl epsiv/n bits, at the cost of /spl epsiv/n invocations of the one-way permutation. The show that this construction is not far from optimal, in the following sense, there exists an oracle relative to which there exists a one-way permutation with inversion probability 2/sup -p(n)/ (for any p(n)/spl isin//spl omega/(log n)), but any construction of an /spl epsiv/n-bit-compressing UOWHF. Requires /spl Omega/(/spl radic/n/p(n)) invocations of the one-way permutation, on average. (For example, there exists in this relativized world a one-way permutation with inversion probability n/sup -/spl omega/(1)/, but no UOWHF that involves it fewer than /spl Omega/(/spl radic/n/log n) times.) Thus any proof that a more efficient UOWHF can be derived from a one-way permutation is necessarily non-relativizing; in particular, no provable construction of a more efficient UOWHF can exist based solely on a "black box" one-way permutation. This result can be viewed as a partial justification for the practice of building efficient UOWHFs from stronger primitives (such as collision intractable hash functions), rather than from weaker primitives such as one-way permutations.
{"title":"Limits on the efficiency of one-way permutation-based hash functions","authors":"J. Kim, Daniel R. Simon, P. Tetali","doi":"10.1109/SFFCS.1999.814627","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814627","url":null,"abstract":"Naor and Yung (1989) show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by /spl epsiv/n bits, at the cost of /spl epsiv/n invocations of the one-way permutation. The show that this construction is not far from optimal, in the following sense, there exists an oracle relative to which there exists a one-way permutation with inversion probability 2/sup -p(n)/ (for any p(n)/spl isin//spl omega/(log n)), but any construction of an /spl epsiv/n-bit-compressing UOWHF. Requires /spl Omega/(/spl radic/n/p(n)) invocations of the one-way permutation, on average. (For example, there exists in this relativized world a one-way permutation with inversion probability n/sup -/spl omega/(1)/, but no UOWHF that involves it fewer than /spl Omega/(/spl radic/n/log n) times.) Thus any proof that a more efficient UOWHF can be derived from a one-way permutation is necessarily non-relativizing; in particular, no provable construction of a more efficient UOWHF can exist based solely on a \"black box\" one-way permutation. This result can be viewed as a partial justification for the practice of building efficient UOWHFs from stronger primitives (such as collision intractable hash functions), rather than from weaker primitives such as one-way permutations.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128640948","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814592
Manindra Agrawal, Somenath Biswas
Gives a simple and new primality testing algorithm by reducing primality testing for a number n to testing if a specific univariate identity over Z/sub n/ holds. We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Z/sub n/ for any n. The running time of the algorithms is polynomial in the size of the arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, e.g. the Schwartz-Zippel test (J.T. Schwartz, 1980; R.E. Zippel, 1979), the Chen-Kao (1997) test and the Lewin-Vadhan (1998) test. Our algorithms first transform the input polynomial to a univariate polynomial and then use Chinese remaindering over univariate polynomials to effectively test if it is zero.
{"title":"Primality and identity testing via Chinese remaindering","authors":"Manindra Agrawal, Somenath Biswas","doi":"10.1109/SFFCS.1999.814592","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814592","url":null,"abstract":"Gives a simple and new primality testing algorithm by reducing primality testing for a number n to testing if a specific univariate identity over Z/sub n/ holds. We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Z/sub n/ for any n. The running time of the algorithms is polynomial in the size of the arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, e.g. the Schwartz-Zippel test (J.T. Schwartz, 1980; R.E. Zippel, 1979), the Chen-Kao (1997) test and the Lewin-Vadhan (1998) test. Our algorithms first transform the input polynomial to a univariate polynomial and then use Chinese remaindering over univariate polynomials to effectively test if it is zero.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132504606","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814626
C. Dwork, M. Naor, Omer Reingold, L. Stockmeyer
In this paper we show that three apparently unrelated problems are in fact very closely related. We sketch these problems at a high level. The selective decommitment problem first arose in a slightly different form, selective decryption, in the context of Byzantine agreement, no later than 1985. Instead of seeing encryptions of plaintexts the adversary is given commitments to the plaintexts. This problem is poorly understood even in strong-receiver commitments, which leak no information about the plaintext values information-theoretically. The second problem is in complexity theory: what can be proved in (a possibly weakened form of) zero-knowledge in a 3-round argument (interactive proof in which the prover is polynomial-time bounded)? The Fiat-Shamir Methodology is cryptographic, and addresses a methodology suggested by Fiat and Shamir (1987) to construct a (non-interactive) signature scheme from any 3-round (not necessarily zero-knowledge) public-coin identification scheme.
{"title":"Magic functions","authors":"C. Dwork, M. Naor, Omer Reingold, L. Stockmeyer","doi":"10.1109/SFFCS.1999.814626","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814626","url":null,"abstract":"In this paper we show that three apparently unrelated problems are in fact very closely related. We sketch these problems at a high level. The selective decommitment problem first arose in a slightly different form, selective decryption, in the context of Byzantine agreement, no later than 1985. Instead of seeing encryptions of plaintexts the adversary is given commitments to the plaintexts. This problem is poorly understood even in strong-receiver commitments, which leak no information about the plaintext values information-theoretically. The second problem is in complexity theory: what can be proved in (a possibly weakened form of) zero-knowledge in a 3-round argument (interactive proof in which the prover is polynomial-time bounded)? The Fiat-Shamir Methodology is cryptographic, and addresses a methodology suggested by Fiat and Shamir (1987) to construct a (non-interactive) signature scheme from any 3-round (not necessarily zero-knowledge) public-coin identification scheme.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130910700","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814617
Avrim Blum, C. Burch, A. Kalai
We construct an online algorithm for paging that achieves an O(r+log k) competitive ratio when compared to an offline strategy that is allowed the additional ability to "rent" pages at a cost of 1/r. In contrast, the competitive ratio of the Marking algorithm for this scenario is O(r log k). Our algorithm can be thought of in the standard setting as having a "fine-grained" competitive ratio, achieving an O(1) ratio when the request sequence consists of a small number of working sets, gracefully decaying to O(log k) as this number increases. Our result is a generalization of the result by Y. Bartal et al. (1997) that one can achieve an O(r+log n) ratio for the unfair n-state uniform-space Metrical Task System problem. That result was a key component of the polylog(n) competitive randomized algorithm given in that paper for the general Metrical Task System problem. One motivation of this work is that it may be a first step toward achieving a polylog(k) randomized competitive ratio for the much more difficult k-server problem.
{"title":"Finely-competitive paging","authors":"Avrim Blum, C. Burch, A. Kalai","doi":"10.1109/SFFCS.1999.814617","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814617","url":null,"abstract":"We construct an online algorithm for paging that achieves an O(r+log k) competitive ratio when compared to an offline strategy that is allowed the additional ability to \"rent\" pages at a cost of 1/r. In contrast, the competitive ratio of the Marking algorithm for this scenario is O(r log k). Our algorithm can be thought of in the standard setting as having a \"fine-grained\" competitive ratio, achieving an O(1) ratio when the request sequence consists of a small number of working sets, gracefully decaying to O(log k) as this number increases. Our result is a generalization of the result by Y. Bartal et al. (1997) that one can achieve an O(r+log n) ratio for the unfair n-state uniform-space Metrical Task System problem. That result was a key component of the polylog(n) competitive randomized algorithm given in that paper for the general Metrical Task System problem. One motivation of this work is that it may be a first step toward achieving a polylog(k) randomized competitive ratio for the much more difficult k-server problem.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126461855","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814618
R. Lipton, Anastasios Viglas
We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often), satisfiability cannot be solved in time O(n/sup 2-/spl epsiv//) and polylogarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of polylogarithmic width computing satisfiability requires infinitely often almost quadratic size.
{"title":"On the complexity of SAT","authors":"R. Lipton, Anastasios Viglas","doi":"10.1109/SFFCS.1999.814618","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814618","url":null,"abstract":"We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often), satisfiability cannot be solved in time O(n/sup 2-/spl epsiv//) and polylogarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of polylogarithmic width computing satisfiability requires infinitely often almost quadratic size.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128761849","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814624
Deborah Goldman, S. Istrail, C. Papadimitriou
We show that calculating contact map overlap (a measure of similarity of protein structures) is NP-hard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the first approximation algorithms with guaranteed error bounds, and NP-completeness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest.
{"title":"Algorithmic aspects of protein structure similarity","authors":"Deborah Goldman, S. Istrail, C. Papadimitriou","doi":"10.1109/SFFCS.1999.814624","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814624","url":null,"abstract":"We show that calculating contact map overlap (a measure of similarity of protein structures) is NP-hard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the first approximation algorithms with guaranteed error bounds, and NP-completeness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132788480","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814572
J. Kleinberg, É. Tardos
In a traditional classification problem, we wish to assign one of k labels (or classes) to each of n objects, in a way that is consistent with some observed data that we have about the problem. An active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified; this issue is one of the principal motivations for the framework of Markov random fields, and it arises in areas such as image processing, biometry: and document analysis. In its most basic form, this style of analysis seeks a classification that optimizes a combinatorial function consisting of assignment costs-based on the individual choice of label we make for each object-and separation costs-based on the pair of choices we make for two "related" objects. We formulate a general classification problem of this type, the metric labeling problem; we show that it contains as special cases a number of standard classification frameworks, including several arising from the theory of Markov random fields. From the perspective of combinatorial optimization, our problem can be viewed as a substantial generalization of the multiway cut problem, and equivalent to a type of uncapacitated quadratic assignment problem. We provide the first non-trivial polynomial-time approximation algorithms for a general family of classification problems of this type. Our main result is an O(log k log log k)-approximation algorithm for the metric labeling problem, with respect to an arbitrary metric on a set of k labels, and an arbitrary weighted graph of relationships on a set of objects. For the special case in which the labels are endowed with the uniform metric-all distances are the same-our methods provide a 2-approximation.
在传统的分类问题中，我们希望为n个对象中的每个对象分配k个标签(或类)中的一个，其方式与我们对问题的一些观察数据一致。这一领域的一个活跃的研究方向是当一个人有关于被分类对象之间的成对关系的信息时进行分类;这个问题是马尔可夫随机场框架的主要动机之一，它出现在图像处理、生物计量和文档分析等领域。在其最基本的形式中，这种风格的分析寻求一种优化组合函数的分类，该组合函数由分配成本(基于我们为每个对象所做的单独标签选择)和分离成本(基于我们为两个“相关”对象所做的成对选择)组成。我们提出了这种类型的一般分类问题，度量标记问题;我们证明了它包含作为特例的一些标准分类框架，其中包括一些由马尔可夫随机场理论产生的分类框架。从组合优化的角度来看，我们的问题可以看作是多路切割问题的一个实质推广，相当于一类无能力二次分配问题。我们提供了第一个非平凡的多项式时间逼近算法，用于这类分类问题的一般族。我们的主要结果是一个O(log k log log k)近似算法，用于度量标记问题，关于k个标记集上的任意度量，以及一组对象上的任意加权关系图。对于标签被赋予一致度量的特殊情况——所有距离都相同——我们的方法提供了一个2近似。
{"title":"Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields","authors":"J. Kleinberg, É. Tardos","doi":"10.1109/SFFCS.1999.814572","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814572","url":null,"abstract":"In a traditional classification problem, we wish to assign one of k labels (or classes) to each of n objects, in a way that is consistent with some observed data that we have about the problem. An active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified; this issue is one of the principal motivations for the framework of Markov random fields, and it arises in areas such as image processing, biometry: and document analysis. In its most basic form, this style of analysis seeks a classification that optimizes a combinatorial function consisting of assignment costs-based on the individual choice of label we make for each object-and separation costs-based on the pair of choices we make for two \"related\" objects. We formulate a general classification problem of this type, the metric labeling problem; we show that it contains as special cases a number of standard classification frameworks, including several arising from the theory of Markov random fields. From the perspective of combinatorial optimization, our problem can be viewed as a substantial generalization of the multiway cut problem, and equivalent to a type of uncapacitated quadratic assignment problem. We provide the first non-trivial polynomial-time approximation algorithms for a general family of classification problems of this type. Our main result is an O(log k log log k)-approximation algorithm for the metric labeling problem, with respect to an arbitrary metric on a set of k labels, and an arbitrary weighted graph of relationships on a set of objects. For the special case in which the labels are endowed with the uniform metric-all distances are the same-our methods provide a 2-approximation.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132677418","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 : 1999-10-17DOI: 10.1109/SFFCS.1999.814609
M. Charikar, S. Guha
We present improved combinatorial approximation algorithms for the uncapacitated facility location and k-median problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2.414+/spl epsiv/ in O/spl tilde/(n/sup 2///spl epsiv/) time. This also yields a bicriteria approximation tradeoff of (1+/spl gamma/, 1+2//spl gamma/) for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to K. Jain and V. Vazirani (1999), we get an approximation ratio of 1.853 in O/spl tilde/(n/sup 3/) time. This is already very close to the approximation guarantee of the best known algorithm which is LP-based. Further combined with the best known LP-based algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728. We present improved approximation algorithms for capacitated facility location and a variant. We also present a 4-approximation for the k-median problem, using similar ideas, building on the 6-approximation of Jain and Vazirani. The algorithm runs in O/spl tilde/(n/sup 3/) time.
{"title":"Improved combinatorial algorithms for the facility location and k-median problems","authors":"M. Charikar, S. Guha","doi":"10.1109/SFFCS.1999.814609","DOIUrl":"https://doi.org/10.1109/SFFCS.1999.814609","url":null,"abstract":"We present improved combinatorial approximation algorithms for the uncapacitated facility location and k-median problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2.414+/spl epsiv/ in O/spl tilde/(n/sup 2///spl epsiv/) time. This also yields a bicriteria approximation tradeoff of (1+/spl gamma/, 1+2//spl gamma/) for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to K. Jain and V. Vazirani (1999), we get an approximation ratio of 1.853 in O/spl tilde/(n/sup 3/) time. This is already very close to the approximation guarantee of the best known algorithm which is LP-based. Further combined with the best known LP-based algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728. We present improved approximation algorithms for capacitated facility location and a variant. We also present a 4-approximation for the k-median problem, using similar ideas, building on the 6-approximation of Jain and Vazirani. The algorithm runs in O/spl tilde/(n/sup 3/) time.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131691781","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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