Efficient algorithms for three-dimensional axial and planar random assignment problems

Frieze, Alan and Sorkin, Gregory B. ORCID: 0000-0003-4935-7820 (2015) Efficient algorithms for three-dimensional axial and planar random assignment problems. Random Structures and Algorithms, 46 (1). 160 - 196. ISSN 1042-9832

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Abstract

Beautiful formulas are known for the expected cost of random two-dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural “Axial” and “Planar” versions, both of which are NP-hard. For 3-dimensional Axial random assignment instances of size n, the cost scales as Ω(1/ n), and a main result of the present paper is a linear-time algorithm that, with high probability, finds a solution of cost O(n–1+o(1)). For 3-dimensional Planar assignment, the lower bound is Ω(n), and we give a new efficient matching-based algorithm that with high probability returns a solution with cost O(n log n).

Item Type:	Article
Official URL:	https://onlinelibrary.wiley.com/journal/10982418
Additional Information:	© 2013 Wiley Periodicals, Inc.
Divisions:	LSE
Subjects:	Q Science > QA Mathematics
Date Deposited:	06 May 2015 08:50
Last Modified:	12 Dec 2024 00:52
Funders:	NSF (CCF-1013110)
URI:	http://eprints.lse.ac.uk/id/eprint/61800

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