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Breaking the
3
/
4
3/4
3/4
Barrier for Approximate Maximin Share
Authors
Hannaneh Akrami
Jugal Garg
Publication date
14 July 2023
Publisher
View
on
arXiv
Abstract
We study the fundamental problem of fairly allocating a set of indivisible goods among
n
n
n
agents with additive valuations using the desirable fairness notion of maximin share (MMS). MMS is the most popular share-based notion, in which an agent finds an allocation fair to her if she receives goods worth at least her MMS value. An allocation is called MMS if all agents receive at least their MMS value. However, since MMS allocations need not exist when
n
>
2
n>2
n
>
2
, a series of works showed the existence of approximate MMS allocations with the current best factor of
3
4
+
O
(
1
n
)
\frac{3}{4} + O(\frac{1}{n})
4
3
β
+
O
(
n
1
β
)
. The recent work by Akrami et al. showed the limitations of existing approaches and proved that they cannot improve this factor to
3
/
4
+
Ξ©
(
1
)
3/4 + \Omega(1)
3/4
+
Ξ©
(
1
)
. In this paper, we bypass these barriers to show the existence of
(
3
4
+
3
3836
)
(\frac{3}{4} + \frac{3}{3836})
(
4
3
β
+
3836
3
β
)
-MMS allocations by developing new reduction rules and analysis techniques
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Full text
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oai:arXiv.org:2307.07304
Last time updated on 20/07/2023