631 research outputs found
Estimating and Sampling Graphs with Multidimensional Random Walks
Estimating characteristics of large graphs via sampling is a vital part of
the study of complex networks. Current sampling methods such as (independent)
random vertex and random walks are useful but have drawbacks. Random vertex
sampling may require too many resources (time, bandwidth, or money). Random
walks, which normally require fewer resources per sample, can suffer from large
estimation errors in the presence of disconnected or loosely connected graphs.
In this work we propose a new -dimensional random walk that uses
dependent random walkers. We show that the proposed sampling method, which we
call Frontier sampling, exhibits all of the nice sampling properties of a
regular random walk. At the same time, our simulations over large real world
graphs show that, in the presence of disconnected or loosely connected
components, Frontier sampling exhibits lower estimation errors than regular
random walks. We also show that Frontier sampling is more suitable than random
vertex sampling to sample the tail of the degree distribution of the graph
Multiple Random Walks to Uncover Short Paths in Power Law Networks
Consider the following routing problem in the context of a large scale
network , with particular interest paid to power law networks, although our
results do not assume a particular degree distribution. A small number of nodes
want to exchange messages and are looking for short paths on . These nodes
do not have access to the topology of but are allowed to crawl the network
within a limited budget. Only crawlers whose sample paths cross are allowed to
exchange topological information. In this work we study the use of random walks
(RWs) to crawl . We show that the ability of RWs to find short paths bears
no relation to the paths that they take. Instead, it relies on two properties
of RWs on power law networks: 1) RW's ability observe a sizable fraction of the
network edges; and 2) an almost certainty that two distinct RW sample paths
cross after a small percentage of the nodes have been visited. We show
promising simulation results on several real world networks
Planting trees in graphs, and finding them back
In this paper we study detection and reconstruction of planted structures in
Erd\H{o}s-R\'enyi random graphs. Motivated by a problem of communication
security, we focus on planted structures that consist in a tree graph. For
planted line graphs, we establish the following phase diagram. In a low density
region where the average degree of the initial graph is below some
critical value , detection and reconstruction go from impossible
to easy as the line length crosses some critical value ,
where is the number of nodes in the graph. In the high density region
, detection goes from impossible to easy as goes from
to , and reconstruction remains impossible so
long as . For -ary trees of varying depth and ,
we identify a low-density region , such that the following
holds. There is a threshold with the following properties.
Detection goes from feasible to impossible as crosses . We also show
that only partial reconstruction is feasible at best for . We
conjecture a similar picture to hold for -ary trees as for lines in the
high-density region , but confirm only the following part of
this picture: Detection is easy for -ary trees of size ,
while at best only partial reconstruction is feasible for -ary trees of any
size . These results are in contrast with the corresponding picture for
detection and reconstruction of {\em low rank} planted structures, such as
dense subgraphs and block communities: We observe a discrepancy between
detection and reconstruction, the latter being impossible for a wide range of
parameters where detection is easy. This property does not hold for previously
studied low rank planted structures
Static assignment of complex stochastic tasks using stochastic majorization
We consider the problem of statically assigning many tasks to a (smaller) system of homogeneous processors, where a task's structure is modeled as a branching process, and all tasks are assumed to have identical behavior. We show how the theory of majorization can be used to obtain a partial order among possible task assignments. Our results show that if the vector of numbers of tasks assigned to each processor under one mapping is majorized by that of another mapping, then the former mapping is better than the latter with respect to a large number of objective functions. In particular, we show how measurements of finishing time, resource utilization, and reliability are all captured by the theory. We also show how the theory may be applied to the problem of partitioning a pool of processors for distribution among parallelizable tasks
Go-With-The-Winner: Client-Side Server Selection for Content Delivery
Content delivery networks deliver much of the web and video content in the
world by deploying a large distributed network of servers. We model and analyze
a simple paradigm for client-side server selection that is commonly used in
practice where each user independently measures the performance of a set of
candidate servers and selects the one that performs the best. For web (resp.,
video) delivery, we propose and analyze a simple algorithm where each user
randomly chooses two or more candidate servers and selects the server that
provided the best hit rate (resp., bit rate). We prove that the algorithm
converges quickly to an optimal state where all users receive the best hit rate
(resp., bit rate), with high probability. We also show that if each user chose
just one random server instead of two, some users receive a hit rate (resp.,
bit rate) that tends to zero. We simulate our algorithm and evaluate its
performance with varying choices of parameters, system load, and content
popularity.Comment: 15 pages, 9 figures, published in IFIP Networking 201
MSPlayer: Multi-Source and multi-Path LeverAged YoutubER
Online video streaming through mobile devices has become extremely popular
nowadays. YouTube, for example, reported that the percentage of its traffic
streaming to mobile devices has soared from 6% to more than 40% over the past
two years. Moreover, people are constantly seeking to stream high quality video
for better experience while often suffering from limited bandwidth. Thanks to
the rapid deployment of content delivery networks (CDNs), popular videos are
now replicated at different sites, and users can stream videos from close-by
locations with low latencies. As mobile devices nowadays are equipped with
multiple wireless interfaces (e.g., WiFi and 3G/4G), aggregating bandwidth for
high definition video streaming has become possible.
We propose a client-based video streaming solution, MSPlayer, that takes
advantage of multiple video sources as well as multiple network paths through
different interfaces. MSPlayer reduces start-up latency and provides high
quality video streaming and robust data transport in mobile scenarios. We
experimentally demonstrate our solution on a testbed and through the YouTube
video service.Comment: accepted to ACM CoNEXT'1
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