Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Welfare-Maximizing Fair Allocations of Indivisible Goods   We study the computational complexity of computing allocations that are both
fair and maximize the utilitarian social welfare, i.e., the sum of agents'
utilities. We focus on two tractable fairness concepts: envy-freeness up to one
item (EF1) and proportionality up to one item (PROP1). In particular, we
consider the following two computational problems: (1) Among the
utilitarian-maximal allocations, decide whether there exists one that is also
fair according to either EF1 or PROP1; (2) among the fair allocations, compute
one that maximizes the utilitarian welfare. We show that both problems are
strongly NP-hard when the number of agents is variable, and remain NP-hard for
a fixed number of agents greater than two. For the special case of two agents,
we find that problem (1) is polynomial-time solvable, while problem (2) remains
NP-hard. Finally, with a fixed number of agents, we design
pseudopolynomial-time algorithms for both problems.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph