580 research outputs found
On graph combinatorics to improve eigenvector-based measures of centrality in directed networks
Producción CientíficaWe present a combinatorial study on the rearrangement of links in the structure of directed networks for the purpose of improving the valuation of a vertex or group of vertices as established by an eigenvector-based centrality measure. We build our topological classification starting from unidirectional rooted trees and up to more complex hierarchical structures such as acyclic digraphs, bidirectional and cyclical rooted trees (obtained by closing cycles on unidirectional trees). We analyze different modifications on the structure of these networks and study their effect on the valuation given by the eigenvector-based scoring functions, with particular focus on α-centrality and PageRank.Ministerio de Economía, Industria y Competitividad (project TIN2014-57226-P)Generalitat de Catalunya (project SGR2014- 890)Ministerio de Ciencia, Innovación y Universidades (project MTM2012-36917-C03-01
On the Approximability of Digraph Ordering
Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute
a labeling maximizing the number of forward edges, i.e.
edges (u,v) such that (u) < (v). For different values of k, this
reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work
studies the approximability of Max-k-Ordering and its generalizations,
motivated by their applications to job scheduling with soft precedence
constraints. We give an LP rounding based 2-approximation algorithm for
Max-k-Ordering for any k={2,..., n}, improving on the known
2k/(k-1)-approximation obtained via random assignment. The tightness of this
rounding is shown by proving that for any k={2,..., n} and constant
, Max-k-Ordering has an LP integrality gap of 2 -
for rounds of the
Sherali-Adams hierarchy.
A further generalization of Max-k-Ordering is the restricted maximum acyclic
subgraph problem or RMAS, where each vertex v has a finite set of allowable
labels . We prove an LP rounding based
approximation for it, improving on the
approximation recently given by Grandoni et al.
(Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact,
our approximation algorithm also works for a general version where the
objective counts the edges which go forward by at least a positive offset
specific to each edge.
The minimization formulation of digraph ordering is DAG edge deletion or
DED(k), which requires deleting the minimum number of edges from an n-vertex
directed acyclic graph (DAG) to remove all paths of length k. We show that
both, the LP relaxation and a local ratio approach for DED(k) yield
k-approximation for any .Comment: 21 pages, Conference version to appear in ESA 201
Functional Integration of Ecological Networks through Pathway Proliferation
Large-scale structural patterns commonly occur in network models of complex
systems including a skewed node degree distribution and small-world topology.
These patterns suggest common organizational constraints and similar functional
consequences. Here, we investigate a structural pattern termed pathway
proliferation. Previous research enumerating pathways that link species
determined that as pathway length increases, the number of pathways tends to
increase without bound. We hypothesize that this pathway proliferation
influences the flow of energy, matter, and information in ecosystems. In this
paper, we clarify the pathway proliferation concept, introduce a measure of the
node--node proliferation rate, describe factors influencing the rate, and
characterize it in 17 large empirical food-webs. During this investigation, we
uncovered a modular organization within these systems. Over half of the
food-webs were composed of one or more subgroups that were strongly connected
internally, but weakly connected to the rest of the system. Further, these
modules had distinct proliferation rates. We conclude that pathway
proliferation in ecological networks reveals subgroups of species that will be
functionally integrated through cyclic indirect effects.Comment: 29 pages, 2 figures, 3 tables, Submitted to Journal of Theoretical
Biolog
Transiently Consistent SDN Updates: Being Greedy is Hard
The software-defined networking paradigm introduces interesting opportunities
to operate networks in a more flexible, optimized, yet formally verifiable
manner. Despite the logically centralized control, however, a Software-Defined
Network (SDN) is still a distributed system, with inherent delays between the
switches and the controller. Especially the problem of changing network
configurations in a consistent manner, also known as the consistent network
update problem, has received much attention over the last years. In particular,
it has been shown that there exists an inherent tradeoff between update
consistency and speed. This paper revisits the problem of updating an SDN in a
transiently consistent, loop-free manner. First, we rigorously prove that
computing a maximum (greedy) loop-free network update is generally NP-hard;
this result has implications for the classic maximum acyclic subgraph problem
(the dual feedback arc set problem) as well. Second, we show that for special
problem instances, fast and good approximation algorithms exist
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