Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse Ranking by Graph Structure: Model and Scalable Algorithms   Distances in a network capture relations between nodes and are the basis of
centrality, similarity, and influence measures. Often, however, the relevance
of a node $u$ to a node $v$ is more precisely measured not by the magnitude of
the distance, but by the number of nodes that are closer to $v$ than $u$. That
is, by the {\em rank} of $u$ in an ordering of nodes by increasing distance
from $v$.
  We identify and address fundamental challenges in rank-based graph mining. We
first consider single-source computation of reverse-ranks and design a
"Dijkstra-like" algorithm which computes nodes in order of increasing
approximate reverse rank while only traversing edges adjacent to returned
nodes. We then define {\em reverse-rank influence}, which naturally extends
reverse nearest neighbors influence [Korn and Muthukrishnan 2000] and builds on
a well studied distance-based influence. We present near-linear algorithms for
greedy approximate reverse-rank influence maximization. The design relies on
our single-source algorithm. Our algorithms utilize near-linear preprocessing
of the network to compute all-distance sketches. As a contribution of
independent interest, we present a novel algorithm for computing these
sketches, which have many other applications, on multi-core architectures.
  We complement our algorithms by establishing the hardness of computing {\em
exact} reverse-ranks for a single source and {\em exact} reverse-rank
influence. This implies that when using near-linear algorithms, the small
relative errors we obtain are the best we can currently hope for.
  Finally, we conduct an experimental evaluation on graphs with tens of
millions of edges, demonstrating both scalability and accuracy.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
2
The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph