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The auction algorithm: A distributed relaxation method for the assignment problem
, 1987
"... We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also ..."
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Cited by 101 (6 self)
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We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also be interpreted as a Jacobi like relaxation method for solving a dual problem. Its (sequential) worst case complexity, for a particular implementation that uses scaling, is O(NAlog(NC)) where N is the number of persons, A is the number of pairs of persons and objects that can be assigned to each other, and C is the maximum absolute object value. Computational results show that, for large problems, the algorithm is competitive with existing methods even without the benefit of parallelism. When executed on a parallel machine, the algorithm exhibits substantial speedup. * Work supported by Grant NSFECS8217668. Thanks are due to J. Kennington and L. Hatay of Southern Methodist Univ. for contributing some of their computational experience. Relaxation methods for optimal network flow problems resemble classical coordinate descent, Jacobi, and GaussSeidel methods for solving unconstrained nonlinear optimization
How to Allocate Network Centers
 J. Algorithms
, 1992
"... This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the significant parameters of center allocation, defines the resulting optimization problems, and proposes several approximation algorithms for selecting centers ..."
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Cited by 77 (4 self)
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This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the significant parameters of center allocation, defines the resulting optimization problems, and proposes several approximation algorithms for selecting centers and for distributing the users among them. We concentrate mainly on balanced versions of the problem, i.e., in which it is required that the assignment of clients to centers be as balanced as possible. The main results are constant ratio approximation algorithms for the balanced centers and balanced weighted centers problems, and logarithmic ratio approximation algorithms for the aedominating set and the ktolerant set problems. School of Library and Information, The Hebrew University, Jerusalem 9xxxx, Israel. This work was carried out while the author was with the Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science. y Department of Applied M...
DUAL COORDINATE STEP METHODS FOR LINEAR NETWORK FLOW PROBLEMS
, 1988
"... We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Int ..."
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Cited by 31 (8 self)
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We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the erelaxation algorithm for the minimumcost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement erelaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
unknown title
, 1992
"... This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the signicant parameters of center allocation, denes the resulting optimization problems, and proposes several approximation algorithms for selecting centers and f ..."
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This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the signicant parameters of center allocation, denes the resulting optimization problems, and proposes several approximation algorithms for selecting centers and for distributing the users among them. We concentrate mainly on balanced versions of the problem, i.e., in which it is required that the assignment of clients to centers be as balanced as possible. The main results are constant ratio approximation algorithms for the balanced centers and balanced weighted centers problems, and logarithmic ratio approximation algorithms for the dominating set and the ktolerant set problems.
RR EC
, 2001
"... A faster data assignment algorithm for maximum likelihoodbased multitarget motion tracking with bearingsonly measurements ..."
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A faster data assignment algorithm for maximum likelihoodbased multitarget motion tracking with bearingsonly measurements
multitarget motion tracking with bearingsonly
, 2001
"... A faster data assignment algorithm for maximum likelihoodbased ..."
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a Security Classification Authority
, 1989
"... A computational comparison of the primal simplex and relaxation algorithms for solving minimum cost flow networks. ..."
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A computational comparison of the primal simplex and relaxation algorithms for solving minimum cost flow networks.