37,877 research outputs found
A Separable Model for Dynamic Networks
Models of dynamic networks --- networks that evolve over time --- have
manifold applications. We develop a discrete-time generative model for social
network evolution that inherits the richness and flexibility of the class of
exponential-family random graph models. The model --- a Separable Temporal ERGM
(STERGM) --- facilitates separable modeling of the tie duration distributions
and the structural dynamics of tie formation. We develop likelihood-based
inference for the model, and provide computational algorithms for maximum
likelihood estimation. We illustrate the interpretability of the model in
analyzing a longitudinal network of friendship ties within a school.Comment: 28 pages (including a 4-page appendix); a substantial rewrite, with
many corrections, changes in terminology, and a different analysis for the
exampl
Networks of Complements
We consider a network of sellers, each selling a single product, where the
graph structure represents pair-wise complementarities between products. We
study how the network structure affects revenue and social welfare of
equilibria of the pricing game between the sellers. We prove positive and
negative results, both of "Price of Anarchy" and of "Price of Stability" type,
for special families of graphs (paths, cycles) as well as more general ones
(trees, graphs). We describe best-reply dynamics that converge to non-trivial
equilibrium in several families of graphs, and we use these dynamics to prove
the existence of approximately-efficient equilibria.Comment: An extended abstract will appear in ICALP 201
Infinite-Duration Bidding Games
Two-player games on graphs are widely studied in formal methods as they model
the interaction between a system and its environment. The game is played by
moving a token throughout a graph to produce an infinite path. There are
several common modes to determine how the players move the token through the
graph; e.g., in turn-based games the players alternate turns in moving the
token. We study the {\em bidding} mode of moving the token, which, to the best
of our knowledge, has never been studied in infinite-duration games. The
following bidding rule was previously defined and called Richman bidding. Both
players have separate {\em budgets}, which sum up to . In each turn, a
bidding takes place: Both players submit bids simultaneously, where a bid is
legal if it does not exceed the available budget, and the higher bidder pays
his bid to the other player and moves the token. The central question studied
in bidding games is a necessary and sufficient initial budget for winning the
game: a {\em threshold} budget in a vertex is a value such that
if Player 's budget exceeds , he can win the game, and if Player 's
budget exceeds , he can win the game. Threshold budgets were previously
shown to exist in every vertex of a reachability game, which have an
interesting connection with {\em random-turn} games -- a sub-class of simple
stochastic games in which the player who moves is chosen randomly. We show the
existence of threshold budgets for a qualitative class of infinite-duration
games, namely parity games, and a quantitative class, namely mean-payoff games.
The key component of the proof is a quantitative solution to strongly-connected
mean-payoff bidding games in which we extend the connection with random-turn
games to these games, and construct explicit optimal strategies for both
players.Comment: A short version appeared in CONCUR 2017. The paper is accepted to
JAC
The Bursty Dynamics of the Twitter Information Network
In online social media systems users are not only posting, consuming, and
resharing content, but also creating new and destroying existing connections in
the underlying social network. While each of these two types of dynamics has
individually been studied in the past, much less is known about the connection
between the two. How does user information posting and seeking behavior
interact with the evolution of the underlying social network structure?
Here, we study ways in which network structure reacts to users posting and
sharing content. We examine the complete dynamics of the Twitter information
network, where users post and reshare information while they also create and
destroy connections. We find that the dynamics of network structure can be
characterized by steady rates of change, interrupted by sudden bursts.
Information diffusion in the form of cascades of post re-sharing often creates
such sudden bursts of new connections, which significantly change users' local
network structure. These bursts transform users' networks of followers to
become structurally more cohesive as well as more homogenous in terms of
follower interests. We also explore the effect of the information content on
the dynamics of the network and find evidence that the appearance of new topics
and real-world events can lead to significant changes in edge creations and
deletions. Lastly, we develop a model that quantifies the dynamics of the
network and the occurrence of these bursts as a function of the information
spreading through the network. The model can successfully predict which
information diffusion events will lead to bursts in network dynamics
Optimal Worst-Case QoS Routing in Constrained AWGN Channel Network
In this paper, we extend the optimal worst-case QoS routing algorithm and metric definition given in [1]. We prove that in addition to the q-ary symmetric and q-ary erasure channel model, the necessary and sufficient conditions defined in [2] for the Generalized Dijkstra's Algorithm (GDA) can be used with a constrained non-negative-mean AWGN channel. The generalization allowed the computation of the worst-case QoS metric value for a given edge weight density. The worst-case value can then be used as the routing metric in networks where some nodes have error correcting capabilities. The result is an optimal worst-case QoS routing algorithm that uses the Generalized Dijkstra's Algorithm as a subroutine with a polynomial time complexity of O(V^3)
An Alternative Approach to the Calculation and Analysis of Connectivity in the World City Network
Empirical research on world cities often draws on Taylor's (2001) notion of
an 'interlocking network model', in which office networks of globalized service
firms are assumed to shape the spatialities of urban networks. In spite of its
many merits, this approach is limited because the resultant adjacency matrices
are not really fit for network-analytic calculations. We therefore propose a
fresh analytical approach using a primary linkage algorithm that produces a
one-mode directed graph based on Taylor's two-mode city/firm network data. The
procedure has the advantage of creating less dense networks when compared to
the interlocking network model, while nonetheless retaining the network
structure apparent in the initial dataset. We randomize the empirical network
with a bootstrapping simulation approach, and compare the simulated parameters
of this null-model with our empirical network parameter (i.e. betweenness
centrality). We find that our approach produces results that are comparable to
those of the standard interlocking network model. However, because our approach
is based on an actual graph representation and network analysis, we are able to
assess cities' position in the network at large. For instance, we find that
cities such as Tokyo, Sydney, Melbourne, Almaty and Karachi hold more strategic
and valuable positions than suggested in the interlocking networks as they play
a bridging role in connecting cities across regions. In general, we argue that
our graph representation allows for further and deeper analysis of the original
data, further extending world city network research into a theory-based
empirical research approach.Comment: 18 pages, 9 figures, 2 table
Spanning Trees with Many Leaves in Graphs without Diamonds and Blossoms
It is known that graphs on n vertices with minimum degree at least 3 have
spanning trees with at least n/4+2 leaves and that this can be improved to
(n+4)/3 for cubic graphs without the diamond K_4-e as a subgraph. We generalize
the second result by proving that every graph with minimum degree at least 3,
without diamonds and certain subgraphs called blossoms, has a spanning tree
with at least (n+4)/3 leaves, and generalize this further by allowing vertices
of lower degree. We show that it is necessary to exclude blossoms in order to
obtain a bound of the form n/3+c.
We use the new bound to obtain a simple FPT algorithm, which decides in
O(m)+O^*(6.75^k) time whether a graph of size m has a spanning tree with at
least k leaves. This improves the best known time complexity for MAX LEAF
SPANNING TREE.Comment: 25 pages, 27 Figure
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