59,881 research outputs found
Balanced Allocation on Graphs: A Random Walk Approach
In this paper we propose algorithms for allocating sequential balls into
bins that are interconnected as a -regular -vertex graph , where
can be any integer.Let be a given positive integer. In each round
, , ball picks a node of uniformly at random and
performs a non-backtracking random walk of length from the chosen node.Then
it allocates itself on one of the visited nodes with minimum load (ties are
broken uniformly at random). Suppose that has a sufficiently large girth
and . Then we establish an upper bound for the maximum number
of balls at any bin after allocating balls by the algorithm, called {\it
maximum load}, in terms of with high probability. We also show that the
upper bound is at most an factor above the lower bound that is
proved for the algorithm. In particular, we show that if we set , for every constant , and
has girth at least , then the maximum load attained by the
algorithm is bounded by with high probability.Finally, we
slightly modify the algorithm to have similar results for balanced allocation
on -regular graph with and sufficiently large girth
Spatial Crowdsourcing Task Allocation Scheme for Massive Data with Spatial Heterogeneity
Spatial crowdsourcing (SC) engages large worker pools for location-based
tasks, attracting growing research interest. However, prior SC task allocation
approaches exhibit limitations in computational efficiency, balanced matching,
and participation incentives. To address these challenges, we propose a
graph-based allocation framework optimized for massive heterogeneous spatial
data. The framework first clusters similar tasks and workers separately to
reduce allocation scale. Next, it constructs novel non-crossing graph
structures to model balanced adjacencies between unevenly distributed tasks and
workers. Based on the graphs, a bidirectional worker-task matching scheme is
designed to produce allocations optimized for mutual interests. Extensive
experiments on real-world datasets analyze the performance under various
parameter settings
The Power Allocation Game on A Network: Balanced Equilibrium
This paper studies a special kind of equilibrium termed as "balanced
equilibrium" which arises in the power allocation game defined in
\cite{allocation}. In equilibrium, each country in antagonism has to use all of
its own power to counteract received threats, and the "threats" made to each
adversary just balance out the threats received from that adversary. This paper
establishes conditions on different types of networked international
environments in order for this equilibrium to exist. The paper also links the
existence of this type of equilibrium on structurally balanced graphs to the
Hall's Maximum Matching problem and the Max Flow problem
The densest subgraph problem in sparse random graphs
We determine the asymptotic behavior of the maximum subgraph density of large
random graphs with a prescribed degree sequence. The result applies in
particular to the Erd\H{o}s-R\'{e}nyi model, where it settles a conjecture of
Hajek [IEEE Trans. Inform. Theory 36 (1990) 1398-1414]. Our proof consists in
extending the notion of balanced loads from finite graphs to their local weak
limits, using unimodularity. This is a new illustration of the objective method
described by Aldous and Steele [In Probability on Discrete Structures (2004)
1-72 Springer].Comment: Published at http://dx.doi.org/10.1214/14-AAP1091 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal Budget Allocation in Social Networks: Quality or Seeding
In this paper, we study a strategic model of marketing and product
consumption in social networks. We consider two competing firms in a market
providing two substitutable products with preset qualities. Agents choose their
consumptions following a myopic best response dynamics which results in a
local, linear update for the consumptions. At some point in time, firms receive
a limited budget which they can use to trigger a larger consumption of their
products in the network. Firms have to decide between marginally improving the
quality of their products and giving free offers to a chosen set of agents in
the network in order to better facilitate spreading their products. We derive a
simple threshold rule for the optimal allocation of the budget and describe the
resulting Nash equilibrium. It is shown that the optimal allocation of the
budget depends on the entire distribution of centralities in the network,
quality of products and the model parameters. In particular, we show that in a
graph with a higher number of agents with centralities above a certain
threshold, firms spend more budget on seeding in the optimal allocation.
Furthermore, if seeding budget is nonzero for a balanced graph, it will also be
nonzero for any other graph, and if seeding budget is zero for a star graph, it
will be zero for any other graph too. We also show that firms allocate more
budget to quality improvement when their qualities are close, in order to
distance themselves from the rival firm. However, as the gap between qualities
widens, competition in qualities becomes less effective and firms spend more
budget on seeding.Comment: 7 page
- …