74,305 research outputs found
The matching polytope does not admit fully-polynomial size relaxation schemes
The groundbreaking work of Rothvo{\ss} [arxiv:1311.2369] established that
every linear program expressing the matching polytope has an exponential number
of inequalities (formally, the matching polytope has exponential extension
complexity). We generalize this result by deriving strong bounds on the
polyhedral inapproximability of the matching polytope: for fixed , every polyhedral -approximation
requires an exponential number of inequalities, where is the number of
vertices. This is sharp given the well-known -approximation of size
provided by the odd-sets of size up to
. Thus matching is the first problem in , whose natural
linear encoding does not admit a fully polynomial-size relaxation scheme (the
polyhedral equivalent of an FPTAS), which provides a sharp separation from the
polynomial-size relaxation scheme obtained e.g., via constant-sized odd-sets
mentioned above.
Our approach reuses ideas from Rothvo{\ss} [arxiv:1311.2369], however the
main lower bounding technique is different. While the original proof is based
on the hyperplane separation bound (also called the rectangle corruption
bound), we employ the information-theoretic notion of common information as
introduced in Braun and Pokutta [http://eccc.hpi-web.de/report/2013/056/],
which allows to analyze perturbations of slack matrices. It turns out that the
high extension complexity for the matching polytope stem from the same source
of hardness as for the correlation polytope: a direct sum structure.Comment: 21 pages, 3 figure
Optimal Information-Theoretic Wireless Location Verification
We develop a new Location Verification System (LVS) focussed on network-based
Intelligent Transport Systems and vehicular ad hoc networks. The algorithm we
develop is based on an information-theoretic framework which uses the received
signal strength (RSS) from a network of base-stations and the claimed position.
Based on this information we derive the optimal decision regarding the
verification of the user's location. Our algorithm is optimal in the sense of
maximizing the mutual information between its input and output data. Our
approach is based on the practical scenario in which a non-colluding malicious
user some distance from a highway optimally boosts his transmit power in an
attempt to fool the LVS that he is on the highway. We develop a practical
threat model for this attack scenario, and investigate in detail the
performance of the LVS in terms of its input/output mutual information. We show
how our LVS decision rule can be implemented straightforwardly with a
performance that delivers near-optimality under realistic threat conditions,
with information-theoretic optimality approached as the malicious user moves
further from the highway. The practical advantages our new
information-theoretic scheme delivers relative to more traditional Bayesian
verification frameworks are discussed.Comment: Corrected typos and introduced new threat model
A Game-Theoretic Framework for Medium Access Control
In this paper, we generalize the random access game model, and show that it provides a general game-theoretic framework for designing contention based medium access control. We extend the random access game model to the network with multiple contention measure signals, study the design of random access games, and analyze different distributed algorithms achieving their equilibria. As examples, a series of utility functions is proposed for games achieving the maximum throughput in a network of homogeneous nodes. In a network with n traffic classes, an N-signal game model is proposed which achieves the maximum throughput under the fairness constraint among different traffic classes. In addition, the convergence of different dynamic algorithms such as best response, gradient play and Jacobi play under propagation delay and estimation error is established. Simulation results show that game model based protocols can achieve superior performance over the standard IEEE 802.11 DCF, and comparable performance as existing protocols with the best performance in literature
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