Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Model of Optimal Network Structure for Decentralized Nearest Neighbor
  Search   One of the approaches for the nearest neighbor search problem is to build a
network which nodes correspond to the given set of indexed objects. In this
case the search of the closest object can be thought as a search of a node in a
network. A procedure in a network is called decentralized if it uses only local
information about visited nodes and its neighbors. Networks, which structure
allows efficient performing the nearest neighbour search by a decentralised
search procedure started from any node, are of particular interest especially
for pure distributed systems. Several algorithms that construct such networks
have been proposed in literature. However, the following questions arise: "Are
there network models in which decentralised search can be performed faster?";
"What are the optimal networks for the decentralised search?"; "What are their
properties?". In this paper we partially give answers to these questions. We
propose a mathematical programming model for the problem of determining an
optimal network structure for decentralized nearest neighbor search. We have
found an exact solution for a regular lattice of size 4x4 and heuristic
solutions for sizes from 5x5 to 7x7. As a distance function we use L1 , L2 and
L_inf metrics. We hope that our results and the proposed model will initiate
study of optimal network structures for decentralised nearest neighbour search.

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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin