6,690 research outputs found
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-HĂŒbner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro PezzĂ©, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Robustness: a New Form of Heredity Motivated by Dynamic Networks
We investigate a special case of hereditary property in graphs, referred to
as {\em robustness}. A property (or structure) is called robust in a graph
if it is inherited by all the connected spanning subgraphs of . We motivate
this definition using two different settings of dynamic networks. The first
corresponds to networks of low dynamicity, where some links may be permanently
removed so long as the network remains connected. The second corresponds to
highly-dynamic networks, where communication links appear and disappear
arbitrarily often, subject only to the requirement that the entities are
temporally connected in a recurrent fashion ({\it i.e.} they can always reach
each other through temporal paths). Each context induces a different
interpretation of the notion of robustness.
We start by motivating the definition and discussing the two interpretations,
after what we consider the notion independently from its interpretation, taking
as our focus the robustness of {\em maximal independent sets} (MIS). A graph
may or may not admit a robust MIS. We characterize the set of graphs \forallMIS
in which {\em all} MISs are robust. Then, we turn our attention to the graphs
that {\em admit} a robust MIS (\existsMIS). This class has a more complex
structure; we give a partial characterization in terms of elementary graph
properties, then a complete characterization by means of a (polynomial time)
decision algorithm that accepts if and only if a robust MIS exists. This
algorithm can be adapted to construct such a solution if one exists
Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization
In this paper, we propose the amphibious influence maximization (AIM) model
that combines traditional marketing via content providers and viral marketing
to consumers in social networks in a single framework. In AIM, a set of content
providers and consumers form a bipartite network while consumers also form
their social network, and influence propagates from the content providers to
consumers and among consumers in the social network following the independent
cascade model. An advertiser needs to select a subset of seed content providers
and a subset of seed consumers, such that the influence from the seed providers
passing through the seed consumers could reach a large number of consumers in
the social network in expectation.
We prove that the AIM problem is NP-hard to approximate to within any
constant factor via a reduction from Feige's k-prover proof system for 3-SAT5.
We also give evidence that even when the social network graph is trivial (i.e.
has no edges), a polynomial time constant factor approximation for AIM is
unlikely. However, when we assume that the weighted bi-adjacency matrix that
describes the influence of content providers on consumers is of constant rank,
a common assumption often used in recommender systems, we provide a
polynomial-time algorithm that achieves approximation ratio of
for any (polynomially small) . Our
algorithmic results still hold for a more general model where cascades in
social network follow a general monotone and submodular function.Comment: An extended abstract appeared in the Proceedings of the 16th ACM
Conference on Economics and Computation (EC), 201
Approximation in stochastic integer programming
Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions. However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality. Only recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.
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