R. Ravi, M. Marathe, S. Ravi, D. Rosenkrantz, H. Hunt
We study network-design problems with multiple design objectives. In particular, we look at two cost measures to be minimized simultaneously: the total cost of the network and the maximum degree of any node in the network. Our main result can be roughly stated as follows: given an integer $b$, we present approximation algorithms for a variety of network-design problems on an $n$-node graph in which the degree of the output network is $O(b log (frac{n}{b}))$ and the cost of this network is $O(log n)$ times that of the minimum-cost degree-$b$-bounded network. These algorithms can handle costs on nodes as well as edges. Moreover, we can construct such networks so as to satisfy a variety of connectivity specifications including spanning trees, Steiner trees and generalized Steiner forests. The performance guarantee on the cost of the output network is nearly best-possible unless $NP = tilde{P}$. We also address the special case in which the costs obey the triangle inequality. In this case, we obtain a polynomial-time approximation algorithm with a stronger performance guarantee. Given a bound $b$ on the degree, the algorithm finds a degree-$b$-bounded network of cost at most a constant time optimum. There is no algorithm that does as well in the absence of triangle inequality unless $P = NP$. We also show that in the case of spanning networks, we can simultaneously approximate within a constant factor yet another objective: the maximum cost of any edge in the network, also called the bottleneck cost of the network. We extend our algorithms to find TSP tours and $k$-connected spanning networks for any fixed $k$ that simultaneously approximate all these three cost measures.
{"title":"Many birds with one stone: multi-objective approximation algorithms","authors":"R. Ravi, M. Marathe, S. Ravi, D. Rosenkrantz, H. Hunt","doi":"10.1145/167088.167209","DOIUrl":"https://doi.org/10.1145/167088.167209","url":null,"abstract":"We study network-design problems with multiple design objectives. In particular, we look at two cost measures to be minimized simultaneously: the total cost of the network and the maximum degree of any node in the network. Our main result can be roughly stated as follows: given an integer $b$, we present approximation algorithms for a variety of network-design problems on an $n$-node graph in which the degree of the output network is $O(b log (frac{n}{b}))$ and the cost of this network is $O(log n)$ times that of the minimum-cost degree-$b$-bounded network. These algorithms can handle costs on nodes as well as edges. Moreover, we can construct such networks so as to satisfy a variety of connectivity specifications including spanning trees, Steiner trees and generalized Steiner forests. The performance guarantee on the cost of the output network is nearly best-possible unless $NP = tilde{P}$. We also address the special case in which the costs obey the triangle inequality. In this case, we obtain a polynomial-time approximation algorithm with a stronger performance guarantee. Given a bound $b$ on the degree, the algorithm finds a degree-$b$-bounded network of cost at most a constant time optimum. There is no algorithm that does as well in the absence of triangle inequality unless $P = NP$. We also show that in the case of spanning networks, we can simultaneously approximate within a constant factor yet another objective: the maximum cost of any edge in the network, also called the bottleneck cost of the network. We extend our algorithms to find TSP tours and $k$-connected spanning networks for any fixed $k$ that simultaneously approximate all these three cost measures.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130766867","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}
We study the problem of counting the number of matchings of given cardinalitg in a d-dimensional rectangular lattice. This problem arises in several models in statistical phgsics, including monomerdimer systems and cell-cluster theory. A classical algorithm due to Fisher, Kasteleyn and Temperley counts perfect matchings exactly in two dimensions, but is not applicable in higher dimensions and does not allow one to count matchings of arbitrary cardinality. In this paper, we present the first eficient approximation algorithms for counting matchings of arbitrary cardinality in (i) d-dimensional ‘>en”odic” lattices (i. e., with wrap-around edges) in any fixed dimension d; and (ii) two-dimensional lattices with “fixed boundary conditions” (i. e., no wrap-around edges). Our technique generalizes to approximately counting matchings in any bipartite graph that is the Cayley graph of some finite group. t CNRS, Ecole Normale Sup&ieure de Lyon, France. Part of this work was done while this author was visiting ICSI, Berkeley. E-mail: kenyon@lip. ens-lyon. f r, $Department of Computer Science, University of California at Berkeley. Supported in part by an AT&T PhD Fellowship and NSF grant CCR88-13632. E-mail: randall@cs. berkeley. edu. $University of Edinburgh and International Computer Science Institute, Berkeley. Supported in part by grant GR/F 90363 of the UK Science and Engineering Research Council. E-mail: sinclairOicsi. berkeley. edu. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed fc,r “direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of tha Association for Computing Machinery. To copy otherwise, or to rapublish, requires a fea and/or specific permission. 25th ACM STOC ‘93-51931CA,WA 01993 ACM 0-89791 -591 -71931000510738 . ..$1 .50 1 Summary 1.1 Background and mot ivation This paper is concerned with the following computational problem: given a finite lattice graph in some fixed number of dimensions, and some number of dominoes, determine the number of ways of placing dominoes on the edges of the graph so that no two dominoes overlap at a vertex. Equivalently, we can think of dominoes as covering a pair of adjacent squares (cubes) in the dual lattice. This is a classical problem in statistical physics, first introduced by Fowler and Rushbrooke in 1937 [3], and is the earliest example of a large class of problems concerned with computing the number of nonoverlapping arrangements of figures of various shapes on a lattice (see, e.g., [11, 16] for a survey). The problem arises in several physical models. For example, in two dimensions the lattice represents the surface of a crystal and the dominoes diatomic molecules (or dimers), and the number of domino arrangements is the number of ways in which a given number of dimers can attach themselves onto the surface; from this inf
{"title":"Matchings in lattice graphs","authors":"Claire Mathieu, Dana Randall, A. Sinclair","doi":"10.1145/167088.167278","DOIUrl":"https://doi.org/10.1145/167088.167278","url":null,"abstract":"We study the problem of counting the number of matchings of given cardinalitg in a d-dimensional rectangular lattice. This problem arises in several models in statistical phgsics, including monomerdimer systems and cell-cluster theory. A classical algorithm due to Fisher, Kasteleyn and Temperley counts perfect matchings exactly in two dimensions, but is not applicable in higher dimensions and does not allow one to count matchings of arbitrary cardinality. In this paper, we present the first eficient approximation algorithms for counting matchings of arbitrary cardinality in (i) d-dimensional ‘>en”odic” lattices (i. e., with wrap-around edges) in any fixed dimension d; and (ii) two-dimensional lattices with “fixed boundary conditions” (i. e., no wrap-around edges). Our technique generalizes to approximately counting matchings in any bipartite graph that is the Cayley graph of some finite group. t CNRS, Ecole Normale Sup&ieure de Lyon, France. Part of this work was done while this author was visiting ICSI, Berkeley. E-mail: kenyon@lip. ens-lyon. f r, $Department of Computer Science, University of California at Berkeley. Supported in part by an AT&T PhD Fellowship and NSF grant CCR88-13632. E-mail: randall@cs. berkeley. edu. $University of Edinburgh and International Computer Science Institute, Berkeley. Supported in part by grant GR/F 90363 of the UK Science and Engineering Research Council. E-mail: sinclairOicsi. berkeley. edu. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed fc,r “direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of tha Association for Computing Machinery. To copy otherwise, or to rapublish, requires a fea and/or specific permission. 25th ACM STOC ‘93-51931CA,WA 01993 ACM 0-89791 -591 -71931000510738 . ..$1 .50 1 Summary 1.1 Background and mot ivation This paper is concerned with the following computational problem: given a finite lattice graph in some fixed number of dimensions, and some number of dominoes, determine the number of ways of placing dominoes on the edges of the graph so that no two dominoes overlap at a vertex. Equivalently, we can think of dominoes as covering a pair of adjacent squares (cubes) in the dual lattice. This is a classical problem in statistical physics, first introduced by Fowler and Rushbrooke in 1937 [3], and is the earliest example of a large class of problems concerned with computing the number of nonoverlapping arrangements of figures of various shapes on a lattice (see, e.g., [11, 16] for a survey). The problem arises in several physical models. For example, in two dimensions the lattice represents the surface of a crystal and the dominoes diatomic molecules (or dimers), and the number of domino arrangements is the number of ways in which a given number of dimers can attach themselves onto the surface; from this inf","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127534832","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 chain of a set P of n points in the plane is a chain of the dominance order on P . A k-chain is a subset C of P that can be covered by k chains. A k-chain C is a maximum k-chain if no other k-chain contains more elements than C. This paper deals with the problem of finding a maximum k-chain of P in the cardinality and in the weighted case. Using the skeleton S(P ) of a point set P introduced by Viennot we describe a fairly simple algorithm that computes maximum k-chains in time O(kn logn) and linear space. The basic idea is that the canonical chain partition of a maximum (k − 1)-chain in the skeleton S(P ) provides k regions in the plane such that a maximum k-chain for P can be obtained as the union of a maximal chain from each of these regions. By the symmetry between chains and antichains in the dominance order we may use the algorithm for maximum k-chains to compute maximum k-antichains for planar points in time O(kn logn). However, for large k one can do better. We describe an algorithm computing maximum k-antichains (and, by symmetry, k-chains) in time O((n2/k) logn) and linear space. Consequently, a maximum k-chain can be computed in time O(n3/2 logn) for arbitrary k. The background for the algorithms is a geometric approach to the Greene–Kleitman theory for permutations. We include a skeleton-based exposition of this theory and give some hints on connections with the theory of Young tableaux. The concept of the skeleton of a planar point set is extended to the case of a weighted point set. This extension allows to compute maximum weighted k-chains with an algorithm that is similar to the algorithm for the cardinality case. The time and space requirements of the algorithm for weighted k-chains are O(2kn log(2kn)) and O(2kn), respectively.
{"title":"Maximum k-chains in planar point sets: combinatorial structure and algorithms","authors":"S. Felsner, L. Wernisch","doi":"10.1145/167088.167136","DOIUrl":"https://doi.org/10.1145/167088.167136","url":null,"abstract":"A chain of a set P of n points in the plane is a chain of the dominance order on P . A k-chain is a subset C of P that can be covered by k chains. A k-chain C is a maximum k-chain if no other k-chain contains more elements than C. This paper deals with the problem of finding a maximum k-chain of P in the cardinality and in the weighted case. Using the skeleton S(P ) of a point set P introduced by Viennot we describe a fairly simple algorithm that computes maximum k-chains in time O(kn logn) and linear space. The basic idea is that the canonical chain partition of a maximum (k − 1)-chain in the skeleton S(P ) provides k regions in the plane such that a maximum k-chain for P can be obtained as the union of a maximal chain from each of these regions. By the symmetry between chains and antichains in the dominance order we may use the algorithm for maximum k-chains to compute maximum k-antichains for planar points in time O(kn logn). However, for large k one can do better. We describe an algorithm computing maximum k-antichains (and, by symmetry, k-chains) in time O((n2/k) logn) and linear space. Consequently, a maximum k-chain can be computed in time O(n3/2 logn) for arbitrary k. The background for the algorithms is a geometric approach to the Greene–Kleitman theory for permutations. We include a skeleton-based exposition of this theory and give some hints on connections with the theory of Young tableaux. The concept of the skeleton of a planar point set is extended to the case of a weighted point set. This extension allows to compute maximum weighted k-chains with an algorithm that is similar to the algorithm for the cardinality case. The time and space requirements of the algorithm for weighted k-chains are O(2kn log(2kn)) and O(2kn), respectively.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"99 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117314420","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}
Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: $$ dst frac{mbox{rm min multicut}}{O(log k)} leq mbox{ rm max flow } leq mbox{ rm min multicut}, $$ noindent where $k$ is the number of commodities. Our proof is constructive; it enables us to find a multicut within $O(log k)$ of the max flow (and hence also the optimal multicut). In addition, the proof technique provides a unified framework in which one can also analyse the case of flows with specified demands of Leighton and Rao and Klein et al. and thereby obtain an improved bound for the latter problem.
考虑多商品流动问题，其目标是使所运输的商品总数最大化。我们证明了以下近似的最大流量最小多切定理:$$ dst frac{mbox{rm min multicut}}{O(log k)} leq mbox{ rm max flow } leq mbox{ rm min multicut}, $$noindent其中$k$为商品数量。我们的证明是建设性的;它使我们能够在最大流量的$O(log k)$内找到一个多路切割(因此也是最佳多路切割)。此外，证明技术提供了一个统一的框架，在这个框架中，人们还可以分析Leighton、Rao和Klein等人具有特定需求的流的情况，从而获得后一个问题的改进界。
{"title":"Approximate max-flow min-(multi)cut theorems and their applications","authors":"Naveen Garg, V. Vazirani, M. Yannakakis","doi":"10.1145/167088.167266","DOIUrl":"https://doi.org/10.1145/167088.167266","url":null,"abstract":"Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: $$ dst frac{mbox{rm min multicut}}{O(log k)} leq mbox{ rm max flow } leq mbox{ rm min multicut}, $$ noindent where $k$ is the number of commodities. Our proof is constructive; it enables us to find a multicut within $O(log k)$ of the max flow (and hence also the optimal multicut). In addition, the proof technique provides a unified framework in which one can also analyse the case of flows with specified demands of Leighton and Rao and Klein et al. and thereby obtain an improved bound for the latter problem.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"352 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124452353","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 constraint-satisfaction problem is given by a pair I (the instance) and T (the template) of finite relational structures over the same vocabulary. The problem is satisfied if there is a homomorphism from 1 to T. It is well-known that the constraintsatisfaction problem is NP-complete. In practice, however, one often encounters the situation where the template T is fixed and it is only the instance I that varies. We define CSP to be the class of constraint-satisfaction problems with respect to fixed templates. It is easy to see that CSP is contained in NP and that CSP contains both problems in P and NP-complete problems. We pose the question whether every problem in CSP is either in P or is NP-complete, and attempt to classify which problems in CSP are in P and which are NP-complete.
{"title":"Monotone monadic SNP and constraint satisfaction","authors":"T. Feder, Moshe Y. Vardi","doi":"10.1145/167088.167245","DOIUrl":"https://doi.org/10.1145/167088.167245","url":null,"abstract":"A constraint-satisfaction problem is given by a pair I (the instance) and T (the template) of finite relational structures over the same vocabulary. The problem is satisfied if there is a homomorphism from 1 to T. It is well-known that the constraintsatisfaction problem is NP-complete. In practice, however, one often encounters the situation where the template T is fixed and it is only the instance I that varies. We define CSP to be the class of constraint-satisfaction problems with respect to fixed templates. It is easy to see that CSP is contained in NP and that CSP contains both problems in P and NP-complete problems. We pose the question whether every problem in CSP is either in P or is NP-complete, and attempt to classify which problems in CSP are in P and which are NP-complete.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125774103","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}
Algorithms for Cache Sharing Daniel Greene * Arvind Raghunathan t A single physical computer memory may be used for more than one type of page, with the amount of memory devoted to each type under software control. For example, the effective size of memory can be increased by storing some pages in compressed form and decompressing on demand. This introduces another level to the memory hierarchy, and the sizes of two adjacent levels may be varied dynamically. We present an algorithm for varying the mixture of pages in a two-type cache, and then analyze the “competitiveness” of our algorithm. We also report progress in partially automating the design and analysis of on-line algorithms.
{"title":"On-line algorithms for cache sharing","authors":"M. Bern, D. Greene, A. Raghunathan","doi":"10.1145/167088.167205","DOIUrl":"https://doi.org/10.1145/167088.167205","url":null,"abstract":"Algorithms for Cache Sharing Daniel Greene * Arvind Raghunathan t A single physical computer memory may be used for more than one type of page, with the amount of memory devoted to each type under software control. For example, the effective size of memory can be increased by storing some pages in compressed form and decompressing on demand. This introduces another level to the memory hierarchy, and the sizes of two adjacent levels may be varied dynamically. We present an algorithm for varying the mixture of pages in a two-type cache, and then analyze the “competitiveness” of our algorithm. We also report progress in partially automating the design and analysis of on-line algorithms.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126984083","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}
This paper presents a polynomial protocol for reaching Byzantine agreement in t + 1 rounds whenever n > 3t, where n is the number of processors and t is an a priori upper bound on the number of failures. This resolves an open problem presented by Pease, Shostak and Lamport ir 1980.
{"title":"Fully polynomial Byzantine agreement in t + 1 rounds","authors":"J. Garay, Y. Moses","doi":"10.1145/167088.167101","DOIUrl":"https://doi.org/10.1145/167088.167101","url":null,"abstract":"This paper presents a polynomial protocol for reaching Byzantine agreement in t + 1 rounds whenever n > 3t, where n is the number of processors and t is an a priori upper bound on the number of failures. This resolves an open problem presented by Pease, Shostak and Lamport ir 1980.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"51 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132477214","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}
We give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating its angles; we also discuss minimality properties of the characterization. The characterization can be used: (1) to decide in linear time whether a given distribution of angles between the edges of a planar triangular graph can result in a planar drawing; (2) to reduce the problem of maximizing the minimum angle in a planar straight-line drawing of a planar triangular graph to a nonlinear optimization problem purely on a space of angles; (3) to give a characterization of the planar drawings of a triconnected graph through a system of equations and inequalities relating its angles; (4) to give a characterization of Delaunay triangulations through a system of equations and inequalities relating its angles; (5) to give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating the lengths of its edges; in turn, this result allows us to give a new characterization of the disc-packing representations of planar triangular graphs.
{"title":"Angles of planar triangular graphs","authors":"G. Battista, L. Vismara","doi":"10.1145/167088.167207","DOIUrl":"https://doi.org/10.1145/167088.167207","url":null,"abstract":"We give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating its angles; we also discuss minimality properties of the characterization. The characterization can be used: (1) to decide in linear time whether a given distribution of angles between the edges of a planar triangular graph can result in a planar drawing; (2) to reduce the problem of maximizing the minimum angle in a planar straight-line drawing of a planar triangular graph to a nonlinear optimization problem purely on a space of angles; (3) to give a characterization of the planar drawings of a triconnected graph through a system of equations and inequalities relating its angles; (4) to give a characterization of Delaunay triangulations through a system of equations and inequalities relating its angles; (5) to give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating the lengths of its edges; in turn, this result allows us to give a new characterization of the disc-packing representations of planar triangular graphs.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132729876","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}
This paper presents a simple local algorithm for load balancing in a distributed network. The algorithm makes no assumption about the structure of the network. It can be executed on a synchronous network with fixed topology, a synchronous network with dynamically changing topology, or an asynchronous network. It works quickly and balances well when the network has an expansion property. In particular, we show that in ann-node network with maximumdegree d whose live edges, at every time step, form a -expander, the algorithm will balance the load to within an additive O(d logn= ) term in O( log(n )= ) time, where is the initial imbalance. The algorithm improves upon previous approaches that yield O(n) time bounds in dynamic and asynchronous networks.
{"title":"Approximate load balancing on dynamic and asynchronous networks","authors":"W. Aiello, B. Awerbuch, B. Maggs, Satish Rao","doi":"10.1145/167088.167250","DOIUrl":"https://doi.org/10.1145/167088.167250","url":null,"abstract":"This paper presents a simple local algorithm for load balancing in a distributed network. The algorithm makes no assumption about the structure of the network. It can be executed on a synchronous network with fixed topology, a synchronous network with dynamically changing topology, or an asynchronous network. It works quickly and balances well when the network has an expansion property. In particular, we show that in ann-node network with maximumdegree d whose live edges, at every time step, form a -expander, the algorithm will balance the load to within an additive O(d logn= ) term in O( log(n )= ) time, where is the initial imbalance. The algorithm improves upon previous approaches that yield O(n) time bounds in dynamic and asynchronous networks.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122882396","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}
In the classical consensus problem,each of n processors receives a private input value and produces a decision value which is one of the original input values,with the requirement that all processors decide the same value. A central result in distributed computing is that,in several standard models including the asynchronous shared-memory model,this problem has no determinis- tic solution. The k-set agreement problem is a generalization of the classical consensus proposed by Chaudhuri (Inform. and Comput.,105 (1993),pp. 132-158),where the agreement condition is weak- ened so that the decision values produced may be different,as long as the number of distinct values is at most k .F or n>k ≥ 2 it was not known whether this problem is solvable deterministically in the asynchronous shared memory model. In this paper,we resolve this question by showing that for any k
{"title":"Wait-free k-set agreement is impossible: the topology of public knowledge","authors":"M. Saks, Fotios Zaharoglou","doi":"10.1145/167088.167122","DOIUrl":"https://doi.org/10.1145/167088.167122","url":null,"abstract":"In the classical consensus problem,each of n processors receives a private input value and produces a decision value which is one of the original input values,with the requirement that all processors decide the same value. A central result in distributed computing is that,in several standard models including the asynchronous shared-memory model,this problem has no determinis- tic solution. The k-set agreement problem is a generalization of the classical consensus proposed by Chaudhuri (Inform. and Comput.,105 (1993),pp. 132-158),where the agreement condition is weak- ened so that the decision values produced may be different,as long as the number of distinct values is at most k .F or n>k ≥ 2 it was not known whether this problem is solvable deterministically in the asynchronous shared memory model. In this paper,we resolve this question by showing that for any k<n ,there is no deterministic wait-free protocol for n processors that solves the k-set agreement problem. The proof technique is new: it is based on the development of a topological structure on the set of possible processor schedules of a protocol. This topological structure has a natural interpretation in terms of the knowledge of the processors of the state of the system. This structure reveals a close analogy between the impossibility of wait-free k-set agreement and the Brouwer fixed point theorem for the k-dimensional ball.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123392913","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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