8,060 research outputs found
Jointly Optimal Routing and Caching for Arbitrary Network Topologies
We study a problem of fundamental importance to ICNs, namely, minimizing
routing costs by jointly optimizing caching and routing decisions over an
arbitrary network topology. We consider both source routing and hop-by-hop
routing settings. The respective offline problems are NP-hard. Nevertheless, we
show that there exist polynomial time approximation algorithms producing
solutions within a constant approximation from the optimal. We also produce
distributed, adaptive algorithms with the same approximation guarantees. We
simulate our adaptive algorithms over a broad array of different topologies.
Our algorithms reduce routing costs by several orders of magnitude compared to
prior art, including algorithms optimizing caching under fixed routing.Comment: This is the extended version of the paper "Jointly Optimal Routing
and Caching for Arbitrary Network Topologies", appearing in the 4th ACM
Conference on Information-Centric Networking (ICN 2017), Berlin, Sep. 26-28,
201
Algorithmic Complexity of Power Law Networks
It was experimentally observed that the majority of real-world networks
follow power law degree distribution. The aim of this paper is to study the
algorithmic complexity of such "typical" networks. The contribution of this
work is twofold.
First, we define a deterministic condition for checking whether a graph has a
power law degree distribution and experimentally validate it on real-world
networks. This definition allows us to derive interesting properties of power
law networks. We observe that for exponents of the degree distribution in the
range such networks exhibit double power law phenomenon that was
observed for several real-world networks. Our observation indicates that this
phenomenon could be explained by just pure graph theoretical properties.
The second aim of our work is to give a novel theoretical explanation why
many algorithms run faster on real-world data than what is predicted by
algorithmic worst-case analysis. We show how to exploit the power law degree
distribution to design faster algorithms for a number of classical P-time
problems including transitive closure, maximum matching, determinant, PageRank
and matrix inverse. Moreover, we deal with the problems of counting triangles
and finding maximum clique. Previously, it has been only shown that these
problems can be solved very efficiently on power law graphs when these graphs
are random, e.g., drawn at random from some distribution. However, it is
unclear how to relate such a theoretical analysis to real-world graphs, which
are fixed. Instead of that, we show that the randomness assumption can be
replaced with a simple condition on the degrees of adjacent vertices, which can
be used to obtain similar results. As a result, in some range of power law
exponents, we are able to solve the maximum clique problem in polynomial time,
although in general power law networks the problem is NP-complete
Ergodic Control and Polyhedral approaches to PageRank Optimization
We study a general class of PageRank optimization problems which consist in
finding an optimal outlink strategy for a web site subject to design
constraints. We consider both a continuous problem, in which one can choose the
intensity of a link, and a discrete one, in which in each page, there are
obligatory links, facultative links and forbidden links. We show that the
continuous problem, as well as its discrete variant when there are no
constraints coupling different pages, can both be modeled by constrained Markov
decision processes with ergodic reward, in which the webmaster determines the
transition probabilities of websurfers. Although the number of actions turns
out to be exponential, we show that an associated polytope of transition
measures has a concise representation, from which we deduce that the continuous
problem is solvable in polynomial time, and that the same is true for the
discrete problem when there are no coupling constraints. We also provide
efficient algorithms, adapted to very large networks. Then, we investigate the
qualitative features of optimal outlink strategies, and identify in particular
assumptions under which there exists a "master" page to which all controlled
pages should point. We report numerical results on fragments of the real web
graph.Comment: 39 page
A literature survey of low-rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as
a new tool in scientific computing to address large-scale linear and
multilinear algebra problems, which would be intractable by classical
techniques. This survey attempts to give a literature overview of current
developments in this area, with an emphasis on function-related tensors
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