88,368 research outputs found
Equivalent relaxations of optimal power flow
Several convex relaxations of the optimal power flow (OPF) problem have
recently been developed using both bus injection models and branch flow models.
In this paper, we prove relations among three convex relaxations: a
semidefinite relaxation that computes a full matrix, a chordal relaxation based
on a chordal extension of the network graph, and a second-order cone relaxation
that computes the smallest partial matrix. We prove a bijection between the
feasible sets of the OPF in the bus injection model and the branch flow model,
establishing the equivalence of these two models and their second-order cone
relaxations. Our results imply that, for radial networks, all these relaxations
are equivalent and one should always solve the second-order cone relaxation.
For mesh networks, the semidefinite relaxation is tighter than the second-order
cone relaxation but requires a heavier computational effort, and the chordal
relaxation strikes a good balance. Simulations are used to illustrate these
results.Comment: 12 pages, 7 figure
On Throughput and Decoding Delay Performance of Instantly Decodable Network Coding
In this paper, a comprehensive study of packet-based instantly decodable
network coding (IDNC) for single-hop wireless broadcast is presented. The
optimal IDNC solution in terms of throughput is proposed and its packet
decoding delay performance is investigated. Lower and upper bounds on the
achievable throughput and decoding delay performance of IDNC are derived and
assessed through extensive simulations. Furthermore, the impact of receivers'
feedback frequency on the performance of IDNC is studied and optimal IDNC
solutions are proposed for scenarios where receivers' feedback is only
available after and IDNC round, composed of several coded transmissions.
However, since finding these IDNC optimal solutions is computational complex,
we further propose simple yet efficient heuristic IDNC algorithms. The impact
of system settings and parameters such as channel erasure probability, feedback
frequency, and the number of receivers is also investigated and simple
guidelines for practical implementations of IDNC are proposed.Comment: This is a 14-page paper submitted to IEEE/ACM Transaction on
Networking. arXiv admin note: text overlap with arXiv:1208.238
Information Recovery from Pairwise Measurements
A variety of information processing tasks in practice involve recovering
objects from single-shot graph-based measurements, particularly those taken
over the edges of some measurement graph . This paper concerns the
situation where each object takes value over a group of different values,
and where one is interested to recover all these values based on observations
of certain pairwise relations over . The imperfection of
measurements presents two major challenges for information recovery: 1)
: a (dominant) portion of measurements are
corrupted; 2) : a significant fraction of pairs are
unobservable, i.e. can be highly sparse.
Under a natural random outlier model, we characterize the , that is, the critical threshold of non-corruption rate
below which exact information recovery is infeasible. This accommodates a very
general class of pairwise relations. For various homogeneous random graph
models (e.g. Erdos Renyi random graphs, random geometric graphs, small world
graphs), the minimax recovery rate depends almost exclusively on the edge
sparsity of the measurement graph irrespective of other graphical
metrics. This fundamental limit decays with the group size at a square root
rate before entering a connectivity-limited regime. Under the Erdos Renyi
random graph, a tractable combinatorial algorithm is proposed to approach the
limit for large (), while order-optimal recovery is
enabled by semidefinite programs in the small regime.
The extended (and most updated) version of this work can be found at
(http://arxiv.org/abs/1504.01369).Comment: This version is no longer updated -- please find the latest version
at (arXiv:1504.01369
Relevance Singular Vector Machine for low-rank matrix sensing
In this paper we develop a new Bayesian inference method for low rank matrix
reconstruction. We call the new method the Relevance Singular Vector Machine
(RSVM) where appropriate priors are defined on the singular vectors of the
underlying matrix to promote low rank. To accelerate computations, a
numerically efficient approximation is developed. The proposed algorithms are
applied to matrix completion and matrix reconstruction problems and their
performance is studied numerically.Comment: International Conference on Signal Processing and Communications
(SPCOM), 5 page
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