13,918 research outputs found
Algorithms for Low-Distortion Embeddings into Arbitrary 1-Dimensional Spaces
We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a "simpler" metric X. Computing such an embedding (exactly or approximately) is a non-trivial task even when X is the metric induced by a path, or, equivalently, the real line. In this paper we give approximation and fixed-parameter tractable (FPT) algorithms for minimum-distortion embeddings into the metric of a subdivision of some fixed graph H, or, equivalently, into any fixed 1-dimensional simplicial complex. More precisely, we study the following problem: For given graphs G, H and integer c, is it possible to embed G with distortion c into a graph homeomorphic to H? Then embedding into the line is the special case H=K_2, and embedding into the cycle is the case H=K_3, where K_k denotes the complete graph on k vertices. For this problem we give
- an approximation algorithm, which in time f(H)* poly (n), for some function f, either correctly decides that there is no embedding of G with distortion c into any graph homeomorphic to H, or finds an embedding with distortion poly(c);
- an exact algorithm, which in time f\u27(H, c)* poly (n), for some function f\u27, either correctly decides that there is no embedding of G with distortion c into any graph homeomorphic to H, or finds an embedding with distortion c. Prior to our work, poly(OPT)-approximation or FPT algorithms were known only for embedding into paths and trees of bounded degrees
FPT-Algorithms for Computing Gromov-Hausdorff and Interleaving Distances Between Trees
The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance between two metric trees. Roughly speaking, a metric tree is a metric space that can be realized by the shortest path metric on a tree. Any finite tree with positive edge weight can be viewed as a metric tree where the weight is treated as edge length and the metric is the induced shortest path metric in the tree. Previously, Agarwal et al. showed that even for trees with unit edge length, it is NP-hard to approximate the Gromov-Hausdorff distance between them within a factor of 3. In this paper, we present a fixed-parameter tractable (FPT) algorithm that can approximate the Gromov-Hausdorff distance between two general metric trees within a multiplicative factor of 14.
Interestingly, the development of our algorithm is made possible by a connection between the Gromov-Hausdorff distance for metric trees and the interleaving distance for the so-called merge trees. The merge trees arise in practice naturally as a simple yet meaningful topological summary (it is a variant of the Reeb graphs and contour trees), and are of independent interest. It turns out that an exact or approximation algorithm for the interleaving distance leads to an approximation algorithm for the Gromov-Hausdorff distance. One of the key contributions of our work is that we re-define the interleaving distance in a way that makes it easier to develop dynamic programming approaches to compute it. We then present a fixed-parameter tractable algorithm to compute the interleaving distance between two merge trees exactly, which ultimately leads to an FPT-algorithm to approximate the Gromov-Hausdorff distance between two metric trees. This exact FPT-algorithm to compute the interleaving distance between merge trees is of interest itself, as it is known that it is NP-hard to approximate it within a factor of 3, and previously the best known algorithm has an approximation factor of O(sqrt{n}) even for trees with unit edge length
Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO
How would a cellular network designed for maximal energy efficiency look
like? To answer this fundamental question, tools from stochastic geometry are
used in this paper to model future cellular networks and obtain a new lower
bound on the average uplink spectral efficiency. This enables us to formulate a
tractable uplink energy efficiency (EE) maximization problem and solve it
analytically with respect to the density of base stations (BSs), the transmit
power levels, the number of BS antennas and users per cell, and the pilot reuse
factor. The closed-form expressions obtained from this general EE maximization
framework provide valuable insights on the interplay between the optimization
variables, hardware characteristics, and propagation environment. Small cells
are proved to give high EE, but the EE improvement saturates quickly with the
BS density. Interestingly, the maximal EE is achieved by also equipping the BSs
with multiple antennas and operate in a "massive MIMO" fashion, where the array
gain from coherent detection mitigates interference and the multiplexing of
many users reduces the energy cost per user.Comment: To appear in IEEE Journal on Selected Areas in Communications, 15
pages, 7 figures, 1 tabl
Designing Wireless Broadband Access for Energy Efficiency: Are Small Cells the Only Answer?
The main usage of cellular networks has changed from voice to data traffic,
mostly requested by static users. In this paper, we analyze how a cellular
network should be designed to provide such wireless broadband access with
maximal energy efficiency (EE). Using stochastic geometry and a detailed power
consumption model, we optimize the density of access points (APs), number of
antennas and users per AP, and transmission power for maximal EE. Small cells
are of course a key technology in this direction, but the analysis shows that
the EE improvement of a small-cell network saturates quickly with the AP
density and then "massive MIMO" techniques can further improve the EE.Comment: Published at Small Cell and 5G Networks (SmallNets) Workshop, IEEE
International Conference on Communications (ICC), 6 pages, 5 figures, 1 tabl
Context-Aware Generative Adversarial Privacy
Preserving the utility of published datasets while simultaneously providing
provable privacy guarantees is a well-known challenge. On the one hand,
context-free privacy solutions, such as differential privacy, provide strong
privacy guarantees, but often lead to a significant reduction in utility. On
the other hand, context-aware privacy solutions, such as information theoretic
privacy, achieve an improved privacy-utility tradeoff, but assume that the data
holder has access to dataset statistics. We circumvent these limitations by
introducing a novel context-aware privacy framework called generative
adversarial privacy (GAP). GAP leverages recent advancements in generative
adversarial networks (GANs) to allow the data holder to learn privatization
schemes from the dataset itself. Under GAP, learning the privacy mechanism is
formulated as a constrained minimax game between two players: a privatizer that
sanitizes the dataset in a way that limits the risk of inference attacks on the
individuals' private variables, and an adversary that tries to infer the
private variables from the sanitized dataset. To evaluate GAP's performance, we
investigate two simple (yet canonical) statistical dataset models: (a) the
binary data model, and (b) the binary Gaussian mixture model. For both models,
we derive game-theoretically optimal minimax privacy mechanisms, and show that
the privacy mechanisms learned from data (in a generative adversarial fashion)
match the theoretically optimal ones. This demonstrates that our framework can
be easily applied in practice, even in the absence of dataset statistics.Comment: Improved version of a paper accepted by Entropy Journal, Special
Issue on Information Theory in Machine Learning and Data Scienc
Can Hardware Distortion Correlation be Neglected When Analyzing Uplink SE in Massive MIMO?
This paper analyzes how the distortion created by hardware impairments in a
multiple-antenna base station affects the uplink spectral efficiency (SE), with
focus on Massive MIMO. The distortion is correlated across the antennas, but
has been often approximated as uncorrelated to facilitate (tractable) SE
analysis. To determine when this approximation is accurate, basic properties of
the distortion correlation are first uncovered. Then, we focus on third-order
non-linearities and prove analytically and numerically that the correlation can
be neglected in the SE analysis when there are many users. In i.i.d. Rayleigh
fading with equal signal-to-noise ratios, this occurs when having five users.Comment: 5 pages, 3 figures, IEEE International Workshop on Signal Processing
Advances in Wireless Communications (SPAWC), 201
Generalized inattentional blindness from a Global Workspace perspective
We apply Baars' Global Workspace model of consciousness to inattentional blindness, using the groupoid network method of Stewart et al. to explore modular structures defined by information measures associated with cognitive process. Internal cross-talk breaks the fundamental groupoid symmetry, and, if sufficiently strong, creates, in a highly punctuated manner, a linked, shifting, giant component which instantiates the global workspace of consciousness. Embedding, exterior, information sources act as an external field which breaks the groupoid symmetry in a somewhat different manner, definng the slowly-acting contexts of Baars' theory and providing topological constraints on the manifestations of consciousness. This analysis significantly extends recent mathematical treatments of the global workspace, and identifies a shifting, topologically-determined syntactical and grammatical 'bottleneck' as a tunable rate distortion manifold which constrains what sensory or other signals can be brought to conscious attention, typically in a punctuated manner. Sensations outside the limits of that filter's syntactic 'bandpass' have lower probability of detection, regardless of their structure, accounting for generalized forms of inattentional blindness
Darwin's Rainbow: Evolutionary radiation and the spectrum of consciousness
Evolution is littered with paraphyletic convergences: many roads lead to functional Romes. We propose here another example - an equivalence class structure factoring the broad realm of possible realizations of the Baars Global Workspace consciousness model. The construction suggests many different physiological systems can support rapidly shifting, sometimes highly tunable, temporary assemblages of interacting unconscious cognitive modules. The discovery implies various animal taxa exhibiting behaviors we broadly recognize as conscious are, in fact, simply expressing different forms of the same underlying phenomenon. Mathematically, we find much slower, and even multiple simultaneous, versions of the basic structure can operate over very long timescales, a kind of paraconsciousness often ascribed to group phenomena. The variety of possibilities, a veritable rainbow, suggests minds today may be only a small surviving fraction of ancient evolutionary radiations - bush phylogenies of consciousness and paraconsciousness. Under this scenario, the resulting diversity was subsequently pruned by selection and chance extinction. Though few traces of the radiation may be found in the direct fossil record, exaptations and vestiges are scattered across the living mind. Humans, for instance, display an uncommonly profound synergism between individual consciousness and their embedding cultural heritages, enabling efficient Lamarkian adaptation
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