2,342 research outputs found
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
Approximate Closest Community Search in Networks
Recently, there has been significant interest in the study of the community
search problem in social and information networks: given one or more query
nodes, find densely connected communities containing the query nodes. However,
most existing studies do not address the "free rider" issue, that is, nodes far
away from query nodes and irrelevant to them are included in the detected
community. Some state-of-the-art models have attempted to address this issue,
but not only are their formulated problems NP-hard, they do not admit any
approximations without restrictive assumptions, which may not always hold in
practice.
In this paper, given an undirected graph G and a set of query nodes Q, we
study community search using the k-truss based community model. We formulate
our problem of finding a closest truss community (CTC), as finding a connected
k-truss subgraph with the largest k that contains Q, and has the minimum
diameter among such subgraphs. We prove this problem is NP-hard. Furthermore,
it is NP-hard to approximate the problem within a factor , for
any . However, we develop a greedy algorithmic framework,
which first finds a CTC containing Q, and then iteratively removes the furthest
nodes from Q, from the graph. The method achieves 2-approximation to the
optimal solution. To further improve the efficiency, we make use of a compact
truss index and develop efficient algorithms for k-truss identification and
maintenance as nodes get eliminated. In addition, using bulk deletion
optimization and local exploration strategies, we propose two more efficient
algorithms. One of them trades some approximation quality for efficiency while
the other is a very efficient heuristic. Extensive experiments on 6 real-world
networks show the effectiveness and efficiency of our community model and
search algorithms
Probabilistic Random Walk Models for Comparative Network Analysis
Graph-based systems and data analysis methods have become critical tools in many
fields as they can provide an intuitive way of representing and analyzing interactions between
variables. Due to the advances in measurement techniques, a massive amount of
labeled data that can be represented as nodes on a graph (or network) have been archived
in databases. Additionally, novel data without label information have been gradually generated
and archived. Labeling and identifying characteristics of novel data is an important
first step in utilizing the valuable data in an effective and meaningful way. Comparative
network analysis is an effective computational means to identify and predict the properties
of the unlabeled data by comparing the similarities and differences between well-studied
and less-studied networks. Comparative network analysis aims to identify the matching
nodes and conserved subnetworks across multiple networks to enable a prediction of the
properties of the nodes in the less-studied networks based on the properties of the matching
nodes in the well-studied networks (i.e., transferring knowledge between networks).
One of the fundamental and important questions in comparative network analysis is
how to accurately estimate node-to-node correspondence as it can be a critical clue in
analyzing the similarities and differences between networks. Node correspondence is a
comprehensive similarity that integrates various types of similarity measurements in a
balanced manner. However, there are several challenges in accurately estimating the node
correspondence for large-scale networks. First, the scale of the networks is a critical issue.
As networks generally include a large number of nodes, we have to examine an extremely
large space and it can pose a computational challenge due to the combinatorial nature of
the problem. Furthermore, although there are matching nodes and conserved subnetworks
in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity.
In this dissertation, novel probabilistic random walk models are proposed to accurately
estimate node-to-node correspondence between networks. First, we propose a context-sensitive
random walk (CSRW) model. In the CSRW model, the random walker analyzes
the context of the current position of the random walker and it can switch the random
movement to either a simultaneous walk on both networks or an individual walk on one
of the networks. The context-sensitive nature of the random walker enables the method
to effectively integrate different types of similarities by dealing with structural variations.
Second, we propose the CUFID (Comparative network analysis Using the steady-state
network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct
an integrated network by inserting pseudo edges between potential matching nodes in
different networks. Then, we design the random walk protocol to transit more frequently
between potential matching nodes as their node similarity increases and they have more
matching neighboring nodes. We apply the proposed random walk models to comparative
network analysis problems: global network alignment and network querying. Through
extensive performance evaluations, we demonstrate that the proposed random walk models
can accurately estimate node correspondence and these can lead to improved and reliable
network comparison results
Probabilistic Random Walk Models for Comparative Network Analysis
Graph-based systems and data analysis methods have become critical tools in many
fields as they can provide an intuitive way of representing and analyzing interactions between
variables. Due to the advances in measurement techniques, a massive amount of
labeled data that can be represented as nodes on a graph (or network) have been archived
in databases. Additionally, novel data without label information have been gradually generated
and archived. Labeling and identifying characteristics of novel data is an important
first step in utilizing the valuable data in an effective and meaningful way. Comparative
network analysis is an effective computational means to identify and predict the properties
of the unlabeled data by comparing the similarities and differences between well-studied
and less-studied networks. Comparative network analysis aims to identify the matching
nodes and conserved subnetworks across multiple networks to enable a prediction of the
properties of the nodes in the less-studied networks based on the properties of the matching
nodes in the well-studied networks (i.e., transferring knowledge between networks).
One of the fundamental and important questions in comparative network analysis is
how to accurately estimate node-to-node correspondence as it can be a critical clue in
analyzing the similarities and differences between networks. Node correspondence is a
comprehensive similarity that integrates various types of similarity measurements in a
balanced manner. However, there are several challenges in accurately estimating the node
correspondence for large-scale networks. First, the scale of the networks is a critical issue.
As networks generally include a large number of nodes, we have to examine an extremely
large space and it can pose a computational challenge due to the combinatorial nature of
the problem. Furthermore, although there are matching nodes and conserved subnetworks
in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity.
In this dissertation, novel probabilistic random walk models are proposed to accurately
estimate node-to-node correspondence between networks. First, we propose a context-sensitive
random walk (CSRW) model. In the CSRW model, the random walker analyzes
the context of the current position of the random walker and it can switch the random
movement to either a simultaneous walk on both networks or an individual walk on one
of the networks. The context-sensitive nature of the random walker enables the method
to effectively integrate different types of similarities by dealing with structural variations.
Second, we propose the CUFID (Comparative network analysis Using the steady-state
network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct
an integrated network by inserting pseudo edges between potential matching nodes in
different networks. Then, we design the random walk protocol to transit more frequently
between potential matching nodes as their node similarity increases and they have more
matching neighboring nodes. We apply the proposed random walk models to comparative
network analysis problems: global network alignment and network querying. Through
extensive performance evaluations, we demonstrate that the proposed random walk models
can accurately estimate node correspondence and these can lead to improved and reliable
network comparison results
Mining Marked Nodes in Large Graphs
abstract: With the rise of the Big Data Era, an exponential amount of network data is being generated at an unprecedented rate across a wide-range of high impact micro and macro areas of research---from protein interaction to social networks. The critical challenge is translating this large scale network data into actionable information.
A key task in the data translation is the analysis of network connectivity via marked nodes---the primary focus of our research. We have developed a framework for analyzing network connectivity via marked nodes in large scale graphs, utilizing novel algorithms in three interrelated areas: (1) analysis of a single seed node via it’s ego-centric network (AttriPart algorithm); (2) pathway identification between two seed nodes (K-Simple Shortest Paths Multithreaded and Search Reduced (KSSPR) algorithm); and (3) tree detection, defining the interaction between three or more seed nodes (Shortest Path MST algorithm).
In an effort to address both fundamental and applied research issues, we have developed the LocalForcasting algorithm to explore how network connectivity analysis can be applied to local community evolution and recommender systems. The goal is to apply the LocalForecasting algorithm to various domains---e.g., friend suggestions in social networks or future collaboration in co-authorship networks. This algorithm utilizes link prediction in combination with the AttriPart algorithm to predict future connections in local graph partitions.
Results show that our proposed AttriPart algorithm finds up to 1.6x denser local partitions, while running approximately 43x faster than traditional local partitioning techniques (PageRank-Nibble). In addition, our LocalForecasting algorithm demonstrates a significant improvement in the number of nodes and edges correctly predicted over baseline methods. Furthermore, results for the KSSPR algorithm demonstrate a speed-up of up to 2.5x the standard k-simple shortest paths algorithm.Dissertation/ThesisMasters Thesis Computer Science 201
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