The complexity of the matroid–greedoid partition problem

We show that the maximum matroid–greedoid partition problem is NP-hard to approximate to within 1 / 2 + ε for any ε > 0 , which matches the trivial factor 1/2 approximation algorithm. The main tool in our hardness of approximation result is an extractor code with polynomial rate, alphabet size an...

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Bibliographic Details
Published in:Theoretical computer science Vol. 410; no. 8; pp. 859 - 866
Main Authors: Asodi, Vera, Umans, Christopher
Format: Journal Article
Language:English
Published: Oxford Elsevier B.V 01.03.2009
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Convex and discrete geometry
Exact sciences and technology
Extractor codes
Fixed-parameter complexity
Geometry
Greedoid
Mathematics
Matroid
Matroid partition problem
Miscellaneous
Sciences and techniques of general use
Theoretical computing
Greedoid
Matroid partition problem
Extractor codes
Matroid
Fixed-parameter complexity
Alphabet
Polynomial
Partition
Construction
Approximation
Computer theory
Decoding
Approximation algorithm
Code
Computational complexity
Maximum
Randomness
Computer
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We show that the maximum matroid–greedoid partition problem is NP-hard to approximate to within 1 / 2 + ε for any ε > 0 , which matches the trivial factor 1/2 approximation algorithm. The main tool in our hardness of approximation result is an extractor code with polynomial rate, alphabet size and list size, together with an efficient algorithm for list-decoding. We show that the recent extractor construction of Guruswami, Umans and Vadhan [V. Guruswami, C. Umans, S.P. Vadhan, Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes, in: IEEE Conference on Computational Complexity, IEEE Computer Society, 2007, pp. 96–108] can be used to obtain a code with these properties. We also show that the parameterized matroid–greedoid partition problem is fixed-parameter tractable.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2008.11.019