Fast exact and approximate algorithms for k-partition and scheduling independent tasks

Chaimovich, M.

doi:10.1016/0012-365x(93)90358-z

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…Recently M. Chaimovich [4] reduced several problems to the subset-sum problem using dense reductions obtaining improved algorithms for these problems. They include the problem of partitioning into k equal parts (for a fixed k) and certain scheduling'problems.…”

Section: Resultsmentioning

confidence: 99%

An almost linear-time algorithm for the dense subset-sum problem

Galil

Margalit

1991

Automata, Languages and Programming

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DenseA b s t r a c t This paper describes a new approach for solving a large subproblem of the subset-sum problem. It is useful for solving other NP-hard integer programming problems. The limits and potential of this approach axe investigated.The approach yields an algorithm for solving the dense version of the subsetsum problem. It runs in time O(£log£), where l is the bound on the size of the elements. But for dense enough inputs and target numbers near the middle sum it runs in time O(m), where m is the number of elements. Consequently, it improves the previously best algorithms by at least one order of magnitude and sometimes by two.The algorithm yields a characterization of the set of subset sums as a collection of arithmetic progressions with the same difference. This characterization is derived by elementary number theoretic and algorithmic techniques. Such a characterization was first obtained by using analytic number theory and yielded inferior algorithms. I n t r o d u c t i o nThere are several ways to cope with the NP-hardness of optimization problems. One is to look for an approximate solution rather than the optimum. There is a vast literature about approximation algorithn~s and approximation schemes. For some problems there are very good approximation algorithms, for others, the problem is still NP-hea'd even ff we settle for an approximate solution. Another way to cope with complexity is to settle for the average case or to allow probabilistic algorithms. There are cases where this approach has paid off and faster algorithms have been discovered. But this has not been the case with NP-hard optimization problems.A third approach of coping with NP-hardness is to try to restrict the problem and design a polynomial-time algorithm, tIere too, there have been mixed results. Some

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Section: Resultsmentioning

confidence: 99%

An almost linear-time algorithm for the dense subset-sum problem

Galil

Margalit

1991

Automata, Languages and Programming

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“…Our objective is to find the segmentation Q * which maximizes (46), i.e., Q * = arg max Q C Q . This is a k-partition problem [19], solvable by dynamic programming. A more interesting performance characterization is as follows.…”

Section: Segmentation Problemmentioning

confidence: 99%

Multicasting Energy and Information Simultaneously

Wu¹,

Tandon

Varshney

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Communication systems for multicasting information and energy simultaneously to more than one user are investigated. In the system under study, a transmitter sends the same message and signal to multiple receivers over distinct and independent channels. The fundamental communication limit under a received energy constraint, called the multicast capacity-energy function, is studied and a single-letter expression is derived. This is based on coding theorems for compound channels. The problem of receiver segmentation, where receivers are divided into related groups, is also considered.

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“…Condition (7) represents the density of a problem in the sense that the number of combinations of unknowns is large with respect to a range of possible values of the linear form. This condition can be strengthened to m > CI1/2 log1//2 £ (see [17] and [22]) , but then the proof becomes quite complicated.…”

Section: Existence Of a Long Interval In A Set Of Subset-sumsmentioning

confidence: 99%

“…Problem. -A structural approach for solving the kpartition problem (KPP) was studied in [7] (see page 346 for problem definition). Although the proposed method works for a wide spectrum of objective functions, the SB author chooses as an objective function the function z =max Under this objective function the problem can also be viewed as a problem of scheduling independent tasks on uniform machines so as to minimize an end (make-span) time (see [21] for scheduling problem definition).…”

Section: N-dimensionalmentioning

confidence: 99%

New Structural Approach to Integer Programming: a Survey

CHAIMOVICH

2018

ast

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L'accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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Fast exact and approximate algorithms for k-partition and scheduling independent tasks

Cited by 4 publications

References 8 publications

An almost linear-time algorithm for the dense subset-sum problem

An almost linear-time algorithm for the dense subset-sum problem

Multicasting Energy and Information Simultaneously

New Structural Approach to Integer Programming: a Survey

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