5160
Well-separated pair decomposition for the unit-disk graph metric and its applications
We extend the classic notion of well-separated pair decomposition [10] to the (weighted) unit-disk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unit-disk graph metric of n points in the plane and for any constant c≥1, there exists a c-well-separated pair decomposition with O(n log n) pairs, and the decomposition can be computed in O(n log n) time. We also show that for the unit-ball graph metric in k dimensions where k≥3, there exists a c-well-separated pair decomposition with O(n2-2/k) pairs, and the bound is tight in the worst case. We present the application of the well-separated pair decomposition in obtaining efficient algorithms for approximating the diameter, closest pair, nearest neighbor, center, median, and stretch factor, all under the unit-disk graph metric.
34184916
Deformable spanners and applications
For a set S of points in ℝ(d), an s-spanner is a subgraph of the complete graph with node set S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)-spanner with O(n/ε(d)) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decompositions, and approximate k-centers.
2954526
Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem
The analysis of incomplete data is a long-standing challenge in practical statistics. When, as is typical, data objects are represented by points in ℝd, incomplete data objects correspond to affine subspaces (lines or Δ-flats). With this motivation we study the problem of finding the minimum intersection radiusr(ℒ) of a set of lines or Δ-flats ℒ: the least r such that there is a ball of radius r intersecting every flat in ℒ. Known algorithms for finding the minimum enclosing ball for a point set (or clustering by several balls) do not easily extend to higher-dimensional flats, primarily because “distances” between flats do not satisfy the triangle inequality. In this paper we show how to restore geometry (i.e., a substitute for the triangle inequality) to the problem, through a new analog of Helly’s theorem. This “intrinsic-dimension” Helly theorem states: for any family ℒ of Δ-dimensional convex sets in a Hilbert space, there exist Δ+2 sets ℒ′⊆ℒ such that r(ℒ)≤2r(ℒ′). Based upon this we present an algorithm that computes a (1+ε)-core set ℒ′⊆ℒ, |ℒ′|=O(Δ4/ε), such that the ball centered at a point c with radius (1+ε)r(ℒ′) intersects every element of ℒ. The running time of the algorithm is O(nΔ+1dpoly (Δ/ε)). For the case of lines or line segments (Δ=1), the (expected) running time of the algorithm can be improved to O(ndpoly (1/ε)). We note that the size of the core set depends only on the dimension of the input objects and is independent of the input size n and the dimension d of the ambient space.
90153
Staying in the Middle: Exact and Approximate Medians in R1 and R2 for Moving Points
Many divide-and-conquer based geometric algorithms and order-statistics problems ask for a point that lies "in the middle" of a given point set. We study several fun- damental problems of this type for moving points in one and two dimensions. In particular, we show how to kinetically maintain the median of a set of n points moving on the real line, and a center point of a set of n points moving in the plane, that is, a point such that any line through it has at most 2n/3 on either side of it. Since the maintenance of exact medians and center points can be quite expensive, we also show how to maintain "-approximate medians and center points and argue that the latter can be made to be much more stable under motion. These results are based on a new algorithm to maintain an "-approximation of a range space under insertions and deletions, which is of independent interest. All our approximation algorithms run in near-linear time.
42656979
Geometric spanner for routing in mobile networks
207794
Trade-Offs between Stretch Factor and Load-Balancing Ratio in Routing on Growth-Restricted Graphs
An unweighted graph has density rho and growth rate k if the number of nodes in every ball with radius r is bounded by rhork. The communication graphs of wireless networks and peer-to-peer networks often have constant bounded density and small growth rate. In this paper, we study the trade-off between two quality measures for routing in growth-restricted graphs. The two measures we consider are the stretch factor, which measures the lengths of the routing paths, and the load-balancing ratio, which measures the evenness of the traffic distribution. We show that if the routing algorithm is required to use paths with stretch factor c, then its load-balancing ratio is bounded by O(rho1/k(n/c)1-1/k), and the bound is tight in the worst case. We show the application and extension of the trade-off to the wireless network routing and VLSI layout design. We also present a load-balanced routing algorithm with the stretch factor constraint in an online setting, in which the routing requests come one by one.
3016958
Multiple frame motion inference using belief propagation
We present an algorithm for automatic inference of human upper body motion. A graph model is proposed for inferring human motion, and motion inference is posed as a mapping problem between state nodes in the graph model and features in image patches. Belief propagation is utilized for Bayesian inference in this graph. A multiple-frame inference model/algorithm is proposed to combine both structural and temporal constraints in human motion. We also present a method for capturing constraints of human body configuration under different view angles. The algorithm is applied in a prototype system that can automatically label upper body motion from videos, without manual initialization of body parts.
9676949
Automatic recognition of eye blinking in spontaneously occurring behavior
Previous research in automatic facial expression recognition has been limited to recognition of gross expression categories (e.g., joy or anger) in posed facial behavior under well-controlled conditions (e.g., frontal pose and minimal out-of-plane head motion). We developed a system that detects discrete and important facial actions, (e.g., eye blinking), in spontaneously occurring facial behavior with non-frontal pose, moderate out-of-plane head motion, and occlusion. The system recovers 3D motion parameters, stabilizes facial regions, extracts motion and appearance information, and recognizes discrete facial actions in spontaneous facial behavior. We tested the system in video data from a 2-person interview. Subjects were ethnically diverse, action units occurred during speech, and out-of-plane motion and occlusion from head motion and glasses were common. The video data were originally collected to answer substantive questions in psychology, and represent a substantial challenge to automated AU recognition. In the analysis of 335 single and multiple blinks and non-blinks, the system achieved 98% accuracy.
11423197
Unsupervised Learning of Dependency Structure for Language Modeling
This paper presents a dependency language model (DLM) that captures linguistic constraints via a dependency structure, i.e., a set of probabilistic dependencies that express the relations between headwords of each phrase in a sentence by an acyclic, planar, undirected graph. Our contributions are three-fold. First, we incorporate the dependency structure into an n-gram language model to capture long distance word dependency. Second, we present an unsupervised learning method that discovers the dependency structure of a sentence using a bootstrapping procedure. Finally, we evaluate the proposed models on a realistic application (Japanese Kana-Kanji conversion). Experiments show that the best DLM achieves an 11.3% error rate reduction over the word trigram model.
15261652
Rendezvous Points-Based Scalable Content Discovery with Load Balancing
ABSTRACT A Content Dis overy System (CDS) enables ontent onsumers to dis over ontent published by ontent providers via a set of ontent resolvers. Existing solutions to CDS systems have diAE ulties in a hieving both ri h fun tionality and s alability. In this paper, we present a distributed and s alable approa h based on Rendezvous Points (RPs) that eAE iently supports exible sear h of dynami ontents. Our system deploys load balan ing matri es (LBMs) to dynami ally balan e registration and query load a ross resolver nodes to maximize system utilization. Our system utilizes existing hash-based algorithms for ontent and query distribution within the overlay resolver network. We use simulation to validate our design.
623541
A multiresolution volume rendering framework for large-scale time-varying data visualization
We present a new parallel multiresolution volume rendering framework for large-scale time-varying data visualization using the wavelet-based time-space partitioning (WTSP) tree. Utilizing the wavelet transform, a large-scale time-varying data set is converted into a space-time multiresolution data hierarchy, and is stored in a time-space partitioning (TSP) tree. To eliminate the parent-child data dependency for reconstruction and achieve load-balanced rendering, we design an algorithm to partition the WTSP tree and distribute the wavelet-compressed data along hierarchical space-filling curves with error-guided bucketization. At run time, the WTSP tree is traversed according to the user-specified time step and tolerances of both spatial and temporal errors. Data blocks of different spatio-temporal resolutions are reconstructed and rendered to compose the final image in parallel. We demonstrate that our algorithm can reduce the run-time communication cost to a minimum and ensure a well-balanced workload among processors when visualizing gigabytes of time-varying data on a PC cluster.