391 research outputs found
TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite
The main result of this work is that an orthogonal access scheme such as TDMA
achieves the all-unicast degrees of freedom (DoF) region of the topological
interference management (TIM) problem if and only if the network topology graph
is chordal bipartite, i.e., every cycle that can contain a chord, does contain
a chord. The all-unicast DoF region includes the DoF region for any arbitrary
choice of a unicast message set, so e.g., the results of Maleki and Jafar on
the optimality of orthogonal access for the sum-DoF of one-dimensional convex
networks are recovered as a special case. The result is also established for
the corresponding topological representation of the index coding problem
Robert's theorem and graphs on complete lattices
Automata networks, and in particular Boolean networks, are used to model
diverse networks of interacting entities. The interaction graph of an automata
network is its most important parameter, as it represents the overall
architecture of the network. A continuous amount of work has been devoted to
infer dynamical properties of the automata network based on its interaction
graph only. Robert's theorem is the seminal result in this area; it states that
automata networks with an acyclic interaction graph converge to a unique fixed
point. The feedback bound can be viewed as an extension of Robert's theorem; it
gives an upper bound on the number of fixed points of an automata network based
on the size of a minimum feedback vertex set of its interaction graph. Boolean
networks can be viewed as self-mappings on the power set lattice of the set of
entities. In this paper, we consider self-mappings on a general complete
lattice. We make two conceptual contributions. Firstly, we can view a digraph
as a residuated mapping on the power set lattice; as such, we define a graph on
a complete lattice as a residuated mapping on that lattice. We extend and
generalise some results on digraphs to our setting. Secondly, we introduce a
generalised notion of dependency whereby any mapping can depend on any
other mapping . In fact, we are able to give four kinds of dependency
in this case. We can then vastly expand Robert's theorem to self-mappings on
general complete lattices; we similarly generalise the feedback bound. We then
obtain stronger results in the case where the lattice is a complete Boolean
algebra. We finally show how our results can be applied to prove the
convergence of automata networks
The average covering tree value for directed graph games
We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, 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
Algorithmic Graph Theory
The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions
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