17,965 research outputs found
Social and place-focused communities in location-based online social networks
Thanks to widely available, cheap Internet access and the ubiquity of
smartphones, millions of people around the world now use online location-based
social networking services. Understanding the structural properties of these
systems and their dependence upon users' habits and mobility has many potential
applications, including resource recommendation and link prediction. Here, we
construct and characterise social and place-focused graphs by using
longitudinal information about declared social relationships and about users'
visits to physical places collected from a popular online location-based social
service. We show that although the social and place-focused graphs are
constructed from the same data set, they have quite different structural
properties. We find that the social and location-focused graphs have different
global and meso-scale structure, and in particular that social and
place-focused communities have negligible overlap. Consequently, group
inference based on community detection performed on the social graph alone
fails to isolate place-focused groups, even though these do exist in the
network. By studying the evolution of tie structure within communities, we show
that the time period over which location data are aggregated has a substantial
impact on the stability of place-focused communities, and that information
about place-based groups may be more useful for user-centric applications than
that obtained from the analysis of social communities alone.Comment: 11 pages, 5 figure
The stable roommates problem with globally-ranked pairs
We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, they can be found in polynomial time. However, it is still the case that strongly stable matchings may not exist, and so we consider the complexity of finding weakly stable matchings with various desirable properties. In particular, we present a polynomial-time algorithm to find a rank-maximal (weakly stable) matching. This is the first generalization of an algorithm due to [Irving et al. 06] to a nonbipartite setting. Also, we describe several hardness results in an even more restricted setting for each of the problems of finding weakly stable matchings that are of maximum size, are egalitarian, have minimum regret, and admit the minimum number of weakly blocking pairs
Constant-factor approximation of near-linear edit distance in near-linear time
We show that the edit distance between two strings of length can be
computed within a factor of in time as long as
the edit distance is at least for some .Comment: 40 pages, 4 figure
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
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