15090068
A simple provable algorithm for curve reconstruction
We present an algorithm that provably reconstructs a curve in the framework introduced by Amenta, Bern and Eppstein. The highlights of the algorithm are: (i) it is simple, (ii) it requires a sampling density better than previously known, (iii) it can be adapted for curve reconstruction in higher dimensions straightforwardly.
7212084
Finding large sticks and potatoes in polygons
We study a class of optimization problems in polygons that seek to compute the "largest" subset of a prescribed type, e.g., a longest line segment ("stick") or a maximum-area triangle or convex body ("potato"). Exact polynomial-time algorithms are known for some of these problems, but their time bounds are high (e.g., O(n7) for the largest convex polygon in a simple n-gon). We devise efficient approximation algorithms for these problems. In particular, we give near-linear time algorithms for a (1 - ∈)-approximation of the biggest stick, an O(1)-approximation of the maximum-area convex body, and a (1 - ∈)-approximation of the maximum-area fat triangle or rectangle. In addition, we give efficient methods for computing large ellipses inside a polygon (whose vertices are a dense sampling of a closed smooth curve). Our algorithms include both deterministic and randomized methods, one of which has been implemented (for computing large area ellipses in a well sampled closed smooth curve).
6513086
Hand Recognition Using Geometric Classifiers
We discuss the issues and challenges in the design of a hand outline based recognition system. Our system is easier to use, cheaper to build and more accurate than previous systems. Extensive tests on more than 700 images collected from 70 people are reported. Classification, verification and identification of the input images were done using two simple geometric classifiers. We describe a novel minimum enclosing ball classifier which performs well for hand recognition and could be of interest for other applications.
29567956
Curve reconstruction from noisy samples
359856
Curve reconstruction from noisy samples
We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.
75138874
An achievable rate for the multiple level relay channel
This paper proposes a new coding scheme and proved a new achievable rate formula for the Gaussian case. The scheme is simpler and avoids some inconvenient techniques (e.g., the Slepian-Wolf partitioning), in giving the same achievable rate for the single relay case. More importantly, this new coding scheme is easier to extend to the multiple level relay case, and generally achieves higher rates. Here we present the results for the discrete memoryless case. The paper also goes on to obtain the capacity of some relay channels under fading, which is the first significant capacity result for such channels, and one, which may possibly constitute a breakthrough in the field.
17708128
Extended message passing algorithm for inference in loopy Gaussian graphical models
Abstract We consider message passing for probabilistic inference in undirected Gaussian graphical models. We show that for singly connected graphs, message passing yields an algorithm that is equivalent to the application of Gaussian elimination to the solution of a particular system of equations. This relation provides a natural way of extending message passing to arbitrary graphs with loops by first studying the operations required by Gaussian elimination. We thus obtain a finite time convergent algorithm that solves the inference problem exactly and whose complexity grows gradually with the “distance” of the graph to a tree. This algorithm can be implemented in a distributed fashion at nodes through message passing, as for example in sensor networks.
769656
Towards an information theory of large networks: an achievable rate region
We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel (DMC). We propose an information-theoretic constructive scheme for obtaining an achievable rate region in such networks. Many well-known capacity-defining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reversely degraded relay channels, the Gaussian multiple-access channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of n nodes located in a region of unit area, we show that a transport capacity of /spl Theta/(n) bit-meters per second (bit-meters/s) is feasible in a certain family of networks, as compared to the best possible transport capacity of /spl Theta/(/spl radic/n) bit-meters/s in Gupta et al. (2000), where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks.
15224609
Codes for Optical CDMA
There has been a recent upsurge of interest in applying Code Division Multiple Access (CDMA) techniques to optical networks. Conventional spreading codes for OCDMA, known as optical orthogonal codes (OOC) spread the signal in the time domain only, which often results in the requirement of a large chip rate. By spreading in both time and wavelength using two-dimensional OOCs, the chip rate can be reduced considerably. This paper presents an overview of 1-D and 2-D optical orthogonal codes as well as some new results relating to bounds on code size and code construction.
7286364
Capacity bounds for ad hoc and hybrid wireless networks
We study the capacity of static wireless networks, both ad hoc and hybrid, under the Protocol and Physical Models of communication, proposed in [1]. For ad hoc networks with <i>n</i> nodes, we show that under the Physical Model, where signal power is assumed to attenuate as 1/r<sup>α</sup>, α > 2, the transport capacity scales as Θ(√<i>n</i>) bit-meters/sec. The same bound holds even when the nodes are allowed to approach arbitrarily close to each other and even under a more generalized notion of the Physical Model wherein the data rate is Shannon's logarithmic function of the SINR at the receiver. This result is sharp since it closes the gap that existed between the previous best known upper bound of O(<i>n</i><sup>α-1/α</sup>) and lower bound of Ω(√n).
 We also show that any spatio-temporal scheduling of transmissions and their ranges that is feasible under the Protocol Model can also be realized under the Physical Model by an appropriate choice of power levels for appropriate thresholds. This allows the generalization of various lower bound constructions from the Protocol Model to the Physical Model. In particular, this provides a better lower bound on the best case transport capacity than in [1].
 For hybrid networks, we consider an overlay of μ<i>n</i> randomly placed wired base stations. It has previously been shown in [6] that if all nodes adopt a common power level, then each node can be provided a throughput of at most Θ(1/log <i>n</i>) to randomly chosen destinations. Here we show that by allowing nodes to perform power control and properly choosing ν(1/log <i>n</i>), it is further possible to provide a throughput of Θ(1) to any fraction <i>f</i>, 0 < <i>f</i> < 1, of nodes. This result holds under both the Protocol and Physical models of communication. On the one hand, it shows that that the aggregate throughput capacity, measured as the sum of individual throughputs, can scale linearly in the number of nodes. On the other hand, the result underscores the importance of choosing minimum power levels for communication and suggests that simply communicating with the closest node or base station could yield good capacity even for multihop hybrid wireless networks.