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Optimization schemes for protective jamming
- In MobiHoc
, 2012
"... In this paper, we study strategies for allocating and man-aging friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i ..."
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In this paper, we study strategies for allocating and man-aging friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i) protecting the privacy of storage locations where RFID tags are used for item identification, (ii) secure reading of RFID tags embedded in credit cards, (iii) protecting data transmitted through wireless networks, sensor networks, etc. By carefully managing jammers to produce noise, we show how to reduce the SINR of eavesdroppers to below a thresh-old for successful reception, without jeopardizing network performance. We present algorithms targeted towards optimizing power allocation and number of jammers needed in several settings. Experimental simulations back up our results.
A Near-Linear Algorithm for Projective Clustering Integer Points
, 2012
"... We consider the problem of projective clustering in Euclidean spaces of non-fixed dimension. Here, we are given a set P of n points in R m and integers j ≥ 1, k ≥ 0, and the goal is to find j k-subspaces so that the sum of the distances of each point in P to the nearest subspace is minimized. Observ ..."
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We consider the problem of projective clustering in Euclidean spaces of non-fixed dimension. Here, we are given a set P of n points in R m and integers j ≥ 1, k ≥ 0, and the goal is to find j k-subspaces so that the sum of the distances of each point in P to the nearest subspace is minimized. Observe that this is a shape fitting problem where we wish to find the best fit in the L1 sense. Here we will treat the number j of subspaces we want to fit and the dimension k of each of them as constants. We consider instances of projective clustering where the point coordinates are integers of magnitude polynomial in m and n. Our main result is a randomized algorithm that for any ε> 0 runs in time O(mn polylog(mn)) and outputs a solution that with high probability is within (1 + ε) of the optimal solution. To obtain this result, we show that the fixed dimensional version of the above projective clustering problem has a small coreset. We do that by observing that in a fairly general sense, shape fitting problems that have small coresets in the L ∞ setting also have small coresets in the L1 setting, and then exploiting an existing construction for the L∞ setting. This observation seems to be quite useful for other shape fitting problems as well, as we demonstrate by constructing the first “regular” coreset for the circle fitting problem in the plane.
An upper bound on the volume of the symmetric difference of a body and a congruent copy
, 2010
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Matching solid shapes in arbitrary dimension via random sampling ∗
, 2012
"... We give simple probabilistic algorithms that approximately maximize the volume of overlap of two solid, i.e. full-dimensional, shapes under translations and rigid motions. The shapes are subsets of Rd where d ≥ 2. The algorithms approximate with respect to an pre-specified additive error and succeed ..."
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We give simple probabilistic algorithms that approximately maximize the volume of overlap of two solid, i.e. full-dimensional, shapes under translations and rigid motions. The shapes are subsets of Rd where d ≥ 2. The algorithms approximate with respect to an pre-specified additive error and succeed with high probability. Apart from measurability assumptions, we only require that points from the shapes can be generated uniformly at random. An important example are shapes given as finite unions of simplices that have pairwise disjoint interiors. 1
Overlap of Convex Polytopes under Rigid Motion
, 2012
"... We present an algorithm to compute an approximate overlap of two convex polytopes P1 and P2 in R³ under rigid motion. Given any ε ∈ (0, 1/2], our algorithm runs in O(ε −3 n log 3.5 n) time with probability 1 − n −O(1) and returns a (1 − ε)-approximate maximum overlap, provided that the maximum overl ..."
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We present an algorithm to compute an approximate overlap of two convex polytopes P1 and P2 in R³ under rigid motion. Given any ε ∈ (0, 1/2], our algorithm runs in O(ε −3 n log 3.5 n) time with probability 1 − n −O(1) and returns a (1 − ε)-approximate maximum overlap, provided that the maximum overlap is at least λ · max{|P1|, |P2|} for some given constant λ ∈ (0, 1].
A generalization of the convex Kakeya problem
- Theoretical Informatics – 10th Latin American Symposium (LATIN 2012
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A Scan Matching Method based on the Area Overlap of Star-Shaped Polygons
"... Abstract-We illustrate a method that performs scan matching by maximizing the intersection area of the scans. The intersection area is a robust parameter that is less prone to measurement errors with respect to alternative techniques. Furthermore, such technique does not require to associate each p ..."
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Abstract-We illustrate a method that performs scan matching by maximizing the intersection area of the scans. The intersection area is a robust parameter that is less prone to measurement errors with respect to alternative techniques. Furthermore, such technique does not require to associate each point of one scan to a point of the other one like in some popular algorithms. The relative pose that maximizes the overlap is estimated iteratively. Since the scans are represented by starshaped polygons due to visibility properties, their intersection can be computed using an efficient linear-time traversal of the vertices. Then, the relative pose is updated under the hypothesis that the combinatorics of intersection is left unchanged and the procedure is repeated until the scans are aligned with sufficient precision.
Approximating the Maximum Overlap of Polygons under Translation
, 2014
"... Let P and Q be two simple polygons in the plane of total complexity n, each of which can be decomposed into at most k convex parts. We present an (1 − ε)-approximation algorithm, for finding the translation of Q, which maximizes its area of overlap with P. Our algorithm runs in O(cn) time, where c i ..."
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Let P and Q be two simple polygons in the plane of total complexity n, each of which can be decomposed into at most k convex parts. We present an (1 − ε)-approximation algorithm, for finding the translation of Q, which maximizes its area of overlap with P. Our algorithm runs in O(cn) time, where c is a constant that depends only on k and ε. This suggest that for polygons that are “close” to being convex, the problem can be solved (approximately), in near linear time.
