Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simpler, faster and shorter labels for distances in graphs   We consider how to assign labels to any undirected graph with n nodes such
that, given the labels of two nodes and no other information regarding the
graph, it is possible to determine the distance between the two nodes. The
challenge in such a distance labeling scheme is primarily to minimize the
maximum label lenght and secondarily to minimize the time needed to answer
distance queries (decoding). Previous schemes have offered different trade-offs
between label lengths and query time. This paper presents a simple algorithm
with shorter labels and shorter query time than any previous solution, thereby
improving the state-of-the-art with respect to both label length and query time
in one single algorithm. Our solution addresses several open problems
concerning label length and decoding time and is the first improvement of label
length for more than three decades.
  More specifically, we present a distance labeling scheme with label size (log
3)/2 + o(n) (logarithms are in base 2) and O(1) decoding time. This outperforms
all existing results with respect to both size and decoding time, including
Winkler's (Combinatorica 1983) decade-old result, which uses labels of size
(log 3)n and O(n/log n) decoding time, and Gavoille et al. (SODA'01), which
uses labels of size 11n + o(n) and O(loglog n) decoding time. In addition, our
algorithm is simpler than the previous ones. In the case of integral edge
weights of size at most W, we present almost matching upper and lower bounds
for label sizes. For r-additive approximation schemes, where distances can be
off by an additive constant r, we give both upper and lower bounds. In
particular, we present an upper bound for 1-additive approximation schemes
which, in the unweighted case, has the same size (ignoring second order terms)
as an adjacency scheme: n/2. We also give results for bipartite graphs and for
exact and 1-additive distance oracles.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol