Efficient algorithms for three-dimensional axial and planar random assignment problems
| Autor: | Gregory B. Sorkin, Alan Frieze |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics Matching (graph theory) Random assignment Efficient algorithm Applied Mathematics General Mathematics Computer Graphics and Computer-Aided Design Upper and lower bounds Planar Computer Science - Data Structures and Algorithms FOS: Mathematics 19999 Mathematical Sciences not elsewhere classified Mathematics - Combinatorics Data Structures and Algorithms (cs.DS) Probabilistic analysis of algorithms QA Mathematics Combinatorics (math.CO) Time complexity Scaling Software Mathematics |
| Zdroj: | Random Structures & Algorithms. 46:160-196 |
| ISSN: | 1042-9832 |
| DOI: | 10.1002/rsa.20525 |
| Popis: | 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) |
| Databáze: | OpenAIRE |
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