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Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
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Cited by 260 (13 self)
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This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques
Approximation algorithms for mixed fractional packing and covering problems
 SIAM J. on Optimization
, 2004
"... Abstract We propose an approximation algorithm based on the Lagrangian or pricedirective decomposition method to compute an¯approximate solution of the mixed fractional packing and covering problem: findÜ�such that�Ü � ¯�,�Ü � ¯�where�Ü��Üare vectors withÅnonnegative convex and concave functions, ..."
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Cited by 9 (3 self)
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Abstract We propose an approximation algorithm based on the Lagrangian or pricedirective decomposition method to compute an¯approximate solution of the mixed fractional packing and covering problem: findÜ�such that�Ü � ¯�,�Ü � ¯�where�Ü��Üare vectors withÅnonnegative convex and concave functions
An Approximation Algorithm for the General Mixed Packing and Covering
 Problem, in "ESCAPE
"... Abstract. We present a pricedirective decomposition algorithm to compute an approximate solution of the mixed packing and covering problem; it either finds x ∈ B such that f(x) ≤ c(1 + ɛ)a and g(x) ≥ (1 − ɛ)b/c or correctly decides that {x ∈ Bf(x) ≤ a, g(x) ≥ b} = ∅. Heref,g are vectors of M ..."
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Cited by 3 (1 self)
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runtime bound independent from c and the input data. Our algorithm is a generalization of [16] and also approximately solves the fractional packing and covering problem where f,g are linear and B is a polytope; there, a widthindependent runtime bound is obtained. 1
Online PrimalDual Algorithms for Covering and Packing Problems
"... We study a wide range of online covering and packing optimization problems. In an online covering problem a linear cost function is known in advance, but the linear constraints that define the feasible solution space are given one by one in an online fashion. In an online packing problem the profit ..."
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Cited by 47 (6 self)
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function as well as the exact packing constraints are not fully known in advance. In each round additional information about the profit function and the constraints is revealed. We provide general deterministic primaldual schemes for online fractional covering and packing problems. We also provide
Integer and fractional packings of hypergraphs
 J. COMBIN. THEORY, SER.B,TOAPPEAR
"... Let F0 be a fixed kuniform hypergraph. The problem of finding the integer F0packing number νF0 (H) of a kuniform hypergraph H is an NPhard problem. Finding the fractional F0packing number ν ∗ (H) however F0 can be done in polynomial time. In this paper we give a lower bound for the integer F0p ..."
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Cited by 4 (1 self)
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Let F0 be a fixed kuniform hypergraph. The problem of finding the integer F0packing number νF0 (H) of a kuniform hypergraph H is an NPhard problem. Finding the fractional F0packing number ν ∗ (H) however F0 can be done in polynomial time. In this paper we give a lower bound for the integer F0
Random Covering and Packing on the Line
, 1982
"... for any Purpose of the United States Government rAcession or NTIS GRA&I 1DTIOX DTIC TAB7o coy unannounced L ..."
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for any Purpose of the United States Government rAcession or NTIS GRA&I 1DTIOX DTIC TAB7o coy unannounced L
Bincompletion algorithms for multicontainer packing, knapsack, and covering problems
 Journal of Artificial Intelligence Research
"... Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multiagent systems and distributed systems, and can also b ..."
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Cited by 12 (5 self)
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of the basic bin completion framework can be enhanced by using a number of extensions, including nogoodbased pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, mincost covering, and bin packing. We show
Faster Approximation Algorithms for Packing and Covering Problems
, 2004
"... We adapt a method proposed by Nesterov [19] to design an algorithm that computes εoptimal solutions to fractional packing problems by solving O*(ε^1 √(Kn)) separable convex quadratic programs, where K is the maximum number of nonzeros per row and n is the number ..."
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Cited by 4 (0 self)
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We adapt a method proposed by Nesterov [19] to design an algorithm that computes εoptimal solutions to fractional packing problems by solving O*(ε^1 √(Kn)) separable convex quadratic programs, where K is the maximum number of nonzeros per row and n is the number
Abstract New Approaches to Covering and Packing Problems
"... Covering and packing integer programs model a large family of combinatorial optimization problems. The currentbest approximation algorithms for these are an instance of the basic probabilistic method: showing that a certain randomized approach produces a good approximation with positive probability ..."
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of these problems. We also present the first NC algorithms for two packing and covering problems that are not subsumed by the above result: finding large independent sets in graphs, and rounding fractional Group Steiner solutions on trees.
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