Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Asymptotically Optimal One-to-One PDP Algorithms for Capacity 2+
  Vehicles   We consider the one-to-one Pickup and Delivery Problem (PDP) in Euclidean
Space with arbitrary dimension $d$ where $n$ transportation requests are picked
i.i.d. with a separate origin-destination pair for each object to be moved.
First, we consider the problem from the customer perspective where the
objective is to compute a plan for transporting the objects such that the
Euclidean distance traveled by the vehicles when carrying objects is minimized.
We develop a polynomial time asymptotically optimal algorithm for vehicles with
capacity $o(\sqrt[2d]{n})$ for this case. This result also holds imposing LIFO
constraints for loading and unloading objects. Secondly, we extend our
algorithm to the classical single-vehicle PDP where the objective is to
minimize the total distance traveled by the vehicle and present results
indicating that the extended algorithm is asymptotically optimal for a fixed
vehicle capacity if the origins and destinations are picked i.i.d. using the
same distribution.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas