Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Complexity of Chore Division   We study the proportional chore division problem where a protocol wants to
divide an undesirable object, called chore, among $n$ different players. The
goal is to find an allocation such that the cost of the chore assigned to each
player be at most $1/n$ of the total cost. This problem is the dual variant of
the cake cutting problem in which we want to allocate a desirable object.
Edmonds and Pruhs showed that any protocol for the proportional cake cutting
must use at least $\Omega(n \log n)$ queries in the worst case, however,
finding a lower bound for the proportional chore division remained an
interesting open problem. We show that chore division and cake cutting problems
are closely related to each other and provide an $\Omega(n \log n)$ lower bound
for chore division.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th