Approximability and exact resolution of the multidimensional binary vector assignment problem

Marin Bougeret (), Guillerme Duvillié () and Rodolphe Giroudeau ()
Additional contact information
Marin Bougeret: LIRMM
Guillerme Duvillié: LIRMM
Rodolphe Giroudeau: LIRMM

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 18, 1059-1073

Abstract: Abstract In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets $$V^1, V^2, \ldots , V^m$$ V 1 , V 2 , … , V m , each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset $$V^i$$ V i . To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by , and the restriction of this problem where every vector has at most c zeros by . was only known to be -hard, even for . We show that, assuming the unique games conjecture, it is -hard to -approximate for any fixed and . This result is tight as any solution is a -approximation. We also prove without assuming UGC that is -hard even for . Finally, we show that is polynomial-time solvable for fixed (which cannot be extended to ).

Keywords: Approximation algorithm; UGC; Inapproximability; Dynamic programming (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-018-0276-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-018-0276-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-018-0276-8

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().