Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to solve the cake-cutting problem in sublinear time   In this paper, we show algorithms for solving the cake-cutting problem in
sublinear-time. More specifically, we preassign (simple) fair portions to o(n)
players in o(n)-time, and minimize the damage to the rest of the players. All
currently known algorithms require Omega(n)-time, even when assigning a portion
to just one player, and it is nontrivial to revise these algorithms to run in
$o(n)$-time since many of the remaining players, who have not been asked any
queries, may not be satisfied with the remaining cake. To challenge this
problem, we begin by providing a framework for solving the cake-cutting problem
in sublinear-time. Generally speaking, solving a problem in sublinear-time
requires the use of approximations. However, in our framework, we introduce the
concept of "eps n-victims," which means that eps n players (victims) may not
get fair portions, where 0< eps =< 1 is an arbitrary constant. In our
framework, an algorithm consists of the following two parts: In the first
(Preassigning) part, it distributes fair portions to r < n players in
o(n)-time. In the second (Completion) part, it distributes fair portions to the
remaining n-r players except for the eps n victims in poly}(n)-time. There are
two variations on the r players in the first part. Specifically, whether they
can or cannot be designated. We will then present algorithms in this framework.
In particular, an O(r/eps)-time algorithm for r =< eps n/127 undesignated
players with eps n-victims, and an O~(r^2/eps)-time algorithm for r =< eps
e^{{sqrt{ln{n}}}/{7}} designated players and eps =< 1/e with eps n-victims are
presented.

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph