Approximation algorithms for integer covering problems via greedy column generation
نویسندگان
چکیده
منابع مشابه
Approximation algorithms for covering/packing integer programs
Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min{cx : x ∈ Z+, Ax ≥ a, Bx ≤ b, x ≤ d}. We give a bicriteria-approximation algorithm that, given ε ∈ (0, 1], finds a solution of cost O(ln(m)/ε) times optimal, meeting the covering constraints (Ax ≥ a) and multiplicity constraints (x ≤ d), and satisfying Bx ≤ (1 + ε)b + β, wher...
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We study a generalization of covering problems called partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial set cover, if each element occurs in at most f sets, then we derive a primal...
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We study the following on-line model for set-covering: elements of a ground set of size n arrive one-by-one and with any such element ci, arrives also the name of some set Si0 containing ci and covering the most of the uncovered ground set-elements (obviously, these elements have not been yet revealed). For this model we analyze a simple greedy algorithm consisting of taking Si0 into the cover,...
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Packing and Covering problems together capture many important problems in combinatorial optimization. We will consider covering problems in these notes. Two canonical covering problems are Vertex Cover and its generalization Set Cover. They play an important role in the study of approximation algorithms. A vertex cover of a graph G = (V,E) is a set S ⊆ V such that for each edge e ∈ E, at least ...
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ژورنال
عنوان ژورنال: RAIRO - Operations Research
سال: 1994
ISSN: 0399-0559,1290-3868
DOI: 10.1051/ro/1994280302831