5298133
Kinetic Medians and kd-Trees
We propose algorithms for maintaining two variants of kd- trees of a set of moving points in the plane. A pseudo kd-tree allows the number of points stored in the two children to differ by a constant factor. An overlapping kd-tree allows the bounding boxes of two children to overlap. We show that both of them support range search operations in O(n1/2+?) time, where ? only depends on the approximation precision. As the points move, we use event-based kinetic data structures to update the tree when necessary. Both trees undergo only a quadratic number of events, which is optimal, and the update cost for each event is only poly-logarithmic. To maintain the pseudo kd-tree, we develop algorithms for computing an approximate median level of a line arrangement, which itself is of great interest. We show that the computation of the approximate median level of a set of lines or line segments can be done in an online fashion smoothly, i.e., there are no expensive updates for any events. For practical consideration, we study the case in which there are speed-limit restrictions or smooth trajectory requirements. The maintenance of the pseudo kd-tree, as a consequence of the approximate median algorithm, can also adapt to those restrictions.
10628567
Shape Segmentation and Applications in Sensor Networks
Many sensor network protocols in the literature implicitly assume that sensor nodes are deployed uniformly inside a simple geometric region. When the real deployment deviates from that, we often observe degraded performance. It is desirable to have a generic approach to handle a sensor field with complex shape. In this paper, we propose a segmentation algorithm that partitions an irregular sensor field into nicely shaped pieces such that algorithms and protocols that assume a nice sensor field can be applied inside each piece. Across the segments, problem dependent structures specify how the segments and data collected in these segments are integrated. This unified topology-adaptive spatial partitioning would benefit many settings that currently assume a nicely shaped sensor field. Our segmentation algorithm does not require sensor locations and only uses network connectivity information. Each node is given a 'flow direction' that directs away from the network boundary. A node with no flow direction becomes a sink, and attracts other nodes in the same segment. We evaluate the performance improvements by integrating shape segmentation with applications such as distributed indices and random sampling.
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.
1839876
Discrete mobile centers
\emph{We propose a new randomized algorithm for maintaining a set of c lusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constant-factor approximation of the minimum possible. As the nodes move, an event-based kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster re-arrangements are avoided. The algorithm can be implemented without exact knowledge of the node positions, if each node is able to sense its distance to other nodes up to the cluster radius. Such a kinetic clustering can be used in numerous applications where mobile devices must be interconnected into an ad-hoc network to collaboratively perform some task.}
45076012
Discrete Mobile Centers 


Abstract. We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constant-factor approximation of the minimum possible. As the nodes move, an event-based kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster re-arrangements are avoided. This clustering algorithm is distributed in nature and can enable numerous applications in ad hoc wireless networks, where mobile devices must be interconnected to perform various tasks collaboratively.

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.
18339723
Automatic video object shape extraction and its classification with camera in motion
In this paper, we present an automatic moving object extraction and classification system. For automatic extraction of object taken by a moving camera, a novel technique is proposed, in which optical flow handles the background modeling and camera motion estimation, and frame difference information yields the exact object shape. We also use forward region boundary based change detection approach for frame difference. This approach assures change detection for uniform intensity regions. For classification, weighted likelihood discriminant based shape classifier is designed. Unlike maximum likelihood (ML) methods, our proposed method utilizes information from all classes to design the classifier. In the description phase of the classifier, curvature features are extracted from the shape and are utilized to build a hidden Markov model (HMM). The HMM provides a robust ML description of the shape. In the discrimination phase, a weighted likelihood discriminant function is introduced, which weights the likelihoods of curvature at individual points of the shape to minimize the classification error. The weights are estimated by generalized probabilistic descent (GPD) method. To demonstrate the performance of the proposed method, we present results achieved for car shapes extraction and classification.
7510303
An adaptive protocol for efficient support of range queries in DHT-based systems
In recent years, distributed hash tables (DHTs) have been proposed as a fundamental building block for large scale distributed applications. Important functionalities such as searching have been added to the DHTs basic lookup capability. However, supporting range queries efficiently remains a difficult problem. We describe an adaptive mechanism that relies on a logical tree data structure, the range search tree (RST), to support range queries efficiently. Nodes in the RST automatically group registrations based on their values. Queries are decomposed into a small number of sub-queries for efficient resolution. The system dynamically optimizes itself to minimize the registration and query cost based on observed load. The system is fully distributed and avoids bottleneck problems encountered in traditional tree-based systems. Extensive simulation results validate the effectiveness of the system.
10392277
Visibility Culling Using Plenoptic Opacity Functions for Large Data Visualization
14303513
A scalable peer-to-peer system for music content and information retrieval
Currently a large percentage of Internet traf£c consists of music £les, typically stored in MP3 compressed audio format, shared and exchanged over Peer-to-Peer (P2P) networks. Searching for music is performed by specifying keywords and naive string matching techniques. In the past years the emerging research area of Music Information Retrieval (MIR) has produced a variety of new ways of looking at the problem of music search. Such MIR techniques can signi£cantly enhance the ways user search for music over P2P networks. In order for that to happen there are two main challenges that need to be addressed: 1) scalability to large collections and number of peers, 2) richer set of search semantics that can support MIR especially when retrieval is content-based. In this paper, we describe a scalable P2P system that uses Rendezvous Points (RPs) for music metadata registration and query resolution, that supports attributevalue search semantics as well as content-based retrieval. The performance of the system has been evaluated in large scale usage scenarios using “real” automatically calculated musical content descriptors.
9243283
Self-occlusion immune video tracking of objects in cluttered environments
We propose a new approach that uses a motion-estimation based framework for video tracking of objects in the presence of self-occlusion in cluttered environments. What makes our work different from others is that, instead of carrying out the motion estimation between two adjacent frames, we tackle the self-occlusion problem from the view of multiple frames. The heart of our approach lies in extracting features appearing in different time frames, genesis frames, and setting up a motion estimation scheme through multiple applications of Kalman filtering based on the different genesis indices. To make the tracked object look visually familiar to the human observer, the system also makes its best attempt at extracting the boundary contour of the object - a difficult problem in its own right, since self-occlusion created by any rotational motion of the tracked object would cause large sections of the boundary contour in the previous frame to disappear in the current frame. Our approach has been tested on a wide variety of video sequences, some of which are presented.