1,510 research outputs found
The Parameterized Complexity of Centrality Improvement in Networks
The centrality of a vertex v in a network intuitively captures how important
v is for communication in the network. The task of improving the centrality of
a vertex has many applications, as a higher centrality often implies a larger
impact on the network or less transportation or administration cost. In this
work we study the parameterized complexity of the NP-complete problems
Closeness Improvement and Betweenness Improvement in which we ask to improve a
given vertex' closeness or betweenness centrality by a given amount through
adding a given number of edges to the network. Herein, the closeness of a
vertex v sums the multiplicative inverses of distances of other vertices to v
and the betweenness sums for each pair of vertices the fraction of shortest
paths going through v. Unfortunately, for the natural parameter "number of
edges to add" we obtain hardness results, even in rather restricted cases. On
the positive side, we also give an island of tractability for the parameter
measuring the vertex deletion distance to cluster graphs
On the fixed-parameter tractability of the maximum connectivity improvement problem
In the Maximum Connectivity Improvement (MCI) problem, we are given a
directed graph and an integer and we are asked to find new
edges to be added to in order to maximize the number of connected pairs of
vertices in the resulting graph. The MCI problem has been studied from the
approximation point of view. In this paper, we approach it from the
parameterized complexity perspective in the case of directed acyclic graphs. We
show several hardness and algorithmic results with respect to different natural
parameters. Our main result is that the problem is -hard for parameter
and it is FPT for parameters and , the matching number of
. We further characterize the MCI problem with respect to other
complementary parameters.Comment: 15 pages, 1 figur
Discriminative Distance-Based Network Indices with Application to Link Prediction
In large networks, using the length of shortest paths as the distance measure
has shortcomings. A well-studied shortcoming is that extending it to
disconnected graphs and directed graphs is controversial. The second
shortcoming is that a huge number of vertices may have exactly the same score.
The third shortcoming is that in many applications, the distance between two
vertices not only depends on the length of shortest paths, but also on the
number of shortest paths. In this paper, first we develop a new distance
measure between vertices of a graph that yields discriminative distance-based
centrality indices. This measure is proportional to the length of shortest
paths and inversely proportional to the number of shortest paths. We present
algorithms for exact computation of the proposed discriminative indices.
Second, we develop randomized algorithms that precisely estimate average
discriminative path length and average discriminative eccentricity and show
that they give -approximations of these indices. Third, we
perform extensive experiments over several real-world networks from different
domains. In our experiments, we first show that compared to the traditional
indices, discriminative indices have usually much more discriminability. Then,
we show that our randomized algorithms can very precisely estimate average
discriminative path length and average discriminative eccentricity, using only
few samples. Then, we show that real-world networks have usually a tiny average
discriminative path length, bounded by a constant (e.g., 2). Fourth, in order
to better motivate the usefulness of our proposed distance measure, we present
a novel link prediction method, that uses discriminative distance to decide
which vertices are more likely to form a link in future, and show its superior
performance compared to the well-known existing measures
Improving information centrality of a node in complex networks by adding edges
The problem of increasing the centrality of a network node arises in many
practical applications. In this paper, we study the optimization problem of
maximizing the information centrality of a given node in a network
with nodes and edges, by creating new edges incident to . Since
is the reciprocal of the sum of resistance distance
between and all nodes, we alternatively consider the problem of minimizing
by adding new edges linked to . We show that the
objective function is monotone and supermodular. We provide a simple greedy
algorithm with an approximation factor and
running time. To speed up the computation, we also present an
algorithm to compute -approximate
resistance distance after iteratively adding edges, the
running time of which is for any
, where the notation suppresses the factors. We experimentally demonstrate the effectiveness and
efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201
GAEA: Graph Augmentation for Equitable Access via Reinforcement Learning
Disparate access to resources by different subpopulations is a prevalent
issue in societal and sociotechnical networks. For example, urban
infrastructure networks may enable certain racial groups to more easily access
resources such as high-quality schools, grocery stores, and polling places.
Similarly, social networks within universities and organizations may enable
certain groups to more easily access people with valuable information or
influence. Here we introduce a new class of problems, Graph Augmentation for
Equitable Access (GAEA), to enhance equity in networked systems by editing
graph edges under budget constraints. We prove such problems are NP-hard, and
cannot be approximated within a factor of . We develop a
principled, sample- and time- efficient Markov Reward Process (MRP)-based
mechanism design framework for GAEA. Our algorithm outperforms baselines on a
diverse set of synthetic graphs. We further demonstrate the method on
real-world networks, by merging public census, school, and transportation
datasets for the city of Chicago and applying our algorithm to find
human-interpretable edits to the bus network that enhance equitable access to
high-quality schools across racial groups. Further experiments on Facebook
networks of universities yield sets of new social connections that would
increase equitable access to certain attributed nodes across gender groups
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