16 research outputs found
Extended h-Index Parameterized Data Structures for Computing Dynamic Subgraph Statistics
We present techniques for maintaining subgraph frequencies in a dynamic
graph, using data structures that are parameterized in terms of h, the h-index
of the graph. Our methods extend previous results of Eppstein and Spiro for
maintaining statistics for undirected subgraphs of size three to directed
subgraphs and to subgraphs of size four. For the directed case, we provide a
data structure to maintain counts for all 3-vertex induced subgraphs in O(h)
amortized time per update. For the undirected case, we maintain the counts of
size-four subgraphs in O(h^2) amortized time per update. These extensions
enable a number of new applications in Bioinformatics and Social Networking
research
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
Assessing the Computational Complexity of Multi-Layer Subgraph Detection
Multi-layer graphs consist of several graphs (layers) over the same vertex
set. They are motivated by real-world problems where entities (vertices) are
associated via multiple types of relationships (edges in different layers). We
chart the border of computational (in)tractability for the class of subgraph
detection problems on multi-layer graphs, including fundamental problems such
as maximum matching, finding certain clique relaxations (motivated by community
detection), or path problems. Mostly encountering hardness results, sometimes
even for two or three layers, we can also spot some islands of tractability
Fast Quasi-Threshold Editing
We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the
quasi-threshold (also called trivially perfect) graph editing problem with edge
insertion and deletion. Given a graph it computes a quasi-threshold graph which
is close in terms of edit count. This edit problem is NP-hard. We present an
extensive experimental study, in which we show that QTM is the first algorithm
that is able to scale to large real-world graphs in practice. As a side result
we further present a simple linear-time algorithm for the quasi-threshold
recognition problem.Comment: 26 pages, 4 figures, submitted to ESA 201
Local community detection based on small cliques
Community detection aims to find dense subgraphs in a network. We consider the problem of finding a community locally around a seed node both in unweighted and weighted networks. This is a faster alternative to algorithms that detect communities that cover the whole network when actually only a single community is required. Further, many overlapping community detection algorithms use local community detection algorithms as basic building block. We provide a broad comparison of different existing strategies of expanding a seed node greedily into a community. For this, we conduct an extensive experimental evaluation both on synthetic benchmark graphs as well as real world networks. We show that results both on synthetic as well as real-world networks can be significantly improved by starting from the largest clique in the neighborhood of the seed node. Further, our experiments indicate that algorithms using scores based on triangles outperform other algorithms in most cases. We provide theoretical descriptions as well as open source implementations of all algorithms used