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The Cartographer
A Quasi-Polynomial Approximation for the Restricted Assignment Problem
January 25, 2017 Β· Declared Dead Β· π Conference on Integer Programming and Combinatorial Optimization
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Authors
Klaus Jansen, Lars Rohwedder
arXiv ID
1701.07208
Category
cs.DS: Data Structures & Algorithms
Citations
24
Venue
Conference on Integer Programming and Combinatorial Optimization
Last Checked
3 months ago
Abstract
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its integrality gap from 1.9142 to 1.8334 and significantly simplify the proof. Then we give a constructive variant, yielding a 1.8334-approximation in quasi-polynomial time. This is the first quasi-polynomial algorithm for this problem improving on the long-standing approximation rate of 2.
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