The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algorithm for estimating the optimal value with the current best for constructing an allocation, there is quite a gap between the ratios that can be achieved in polynomial time: 4+delta for estimation and 6 + 2 sqrt{10} + delta ~~ 12.325 + delta for construction, where delta is an arbitrarily small constant greater than 0. We propose an algorithm that constructs an allocation with value within a factor 6 + delta from the optimum for any constant delta > 0. The running time is polynomial in the input size for any constant delta chosen.
@InProceedings{cheng_et_al:LIPIcs.ICALP.2018.37, author = {Cheng, Siu-Wing and Mao, Yuchen}, title = {{Restricted Max-Min Fair Allocation}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {37:1--37:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.37}, URN = {urn:nbn:de:0030-drops-90418}, doi = {10.4230/LIPIcs.ICALP.2018.37}, annote = {Keywords: Fair allocation, approximation, local search} }
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