Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse Shortest Path Problem for Unit-Disk Graphs   Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with
respect to a parameter r is an undirected graph whose vertex set is P such that
an edge connects two points p, q \in P if the Euclidean distance between p and
q is at most r (the weight of the edge is 1 in the unweighted case and is the
distance between p and q in the weighted case). Given a value \lambda>0 and two
points s and t of P, we consider the following reverse shortest path problem:
computing the smallest r such that the shortest path length between s and t in
G_r(P) is at most \lambda. In this paper, we present an algorithm of O(\lfloor
\lambda \rfloor \cdot n \log n) time and another algorithm of O(n^{5/4}
\log^{7/4} n) time for the unweighted case, as well as an O(n^{5/4} \log^{5/2}
n) time algorithm for the weighted case. We also consider the L_1 version of
the problem where the distance of two points is measured by the L_1 metric; we
solve the problem in O(n \log^3 n) time for both the unweighted and weighted
cases.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph