Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Approximate Shortest Paths in the Congested Clique   We design fast deterministic algorithms for distance computation in the
congested clique model. Our key contributions include:
  -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in
$O(\log^2{n} / \epsilon)$ rounds on unweighted undirected graphs. With a small
additional additive factor, this also applies for weighted graphs. This is the
first sub-polynomial constant-factor approximation for APSP in this model.
  -- A $(1+\epsilon)$-approximation for multi-source shortest paths from
$O(\sqrt{n})$ sources in $O(\log^2{n} / \epsilon)$ rounds on weighted
undirected graphs. This is the first sub-polynomial algorithm obtaining this
approximation for a set of sources of polynomial size.
  Our main techniques are new distance tools that are obtained via improved
algorithms for sparse matrix multiplication, which we leverage to construct
efficient hopsets and shortest paths. Furthermore, our techniques extend to
additional distance problems for which we improve upon the state-of-the-art,
including diameter approximation, and an exact single-source shortest paths
algorithm for weighted undirected graphs in $\tilde{O}(n^{1/6})$ rounds.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci