174192
Fault tolerant networks with small degree
In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph <italic>G</italic> (linear array or mesh in this paper), a graph <italic>G</italic>′ is called a &kgr;-fault-tolerant graph of <italic>G</italic> if when we remove any &kgr; nodes from <italic>G</italic>′, it still contains a subgraph isomorphic to <italic>G</italic>. The major quality measures for a fault-tolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree <italic>O</italic>(1) for arrays and <italic>O</italic>(log<supscrpt>3</supscrpt> &kgr;) for meshes. The number of spare nodes used are <italic>O</italic>(&kgr; log<supscrpt>2</supscrpt> &kgr;) and <italic>O</italic>(&kgr;<supscrpt>2</supscrpt>/log &kgr;), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in &kgr;.
8360631
Kinetic Connectivity for Unit Disks
We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unit-radius disks moving in the plane. We assume that the motion of each disk can be specified by a low-degree algebraic trajectory; this trajectory, however, can be modified in an on-line fashion. While the disks move continuously, their connectivity changes at discrete times. Our main result is an O(n) space data structure that takes O(log  n\slash \kern -1pt log log  n) time per connectivity query of the form ``are disks A and B in the same connected component?’’ A straightforward approach based on dynamically maintaining the overlap graph requires Ω (n2) space. Our data structure requires only linear space and must deal with O(n2 + ε) updates in the worst case, each requiring O(log 2 n) amortized time, for any ε>0 . This number of updates is close to optimal, since a set of n moving unit disks can undergo Ω (n2) connectivity changes.
9779472
H-Walk: hierarchical distance computation for moving convex bodies
This paper presents the Hierarchical Walk, or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. For convex polygons, we prove that H-Walk improves on the classic Lin-Canny and DobkinKirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. Experimental results indicate that, unlike previous incremental distance computation algorithms, H-Walk adapts well to variable coherence in the motion.
591702
Compact Voronoi Diagrams for Moving Convex Polygons
We describe a kinetic data structure for maintaining a compact Voronoi-like diagram of convex polygons moving around in the plane. We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96]. A key feature of this diagram is that its size is only a function of the number of polygons and not of their complexity. We demonstrate a local certifying property of that diagram, akin to that of Delaunay triangulations of points. We then obtain a method for maintaining this diagram that is output-sensitive and costs O(log n) per update. Furthermore, we show that for a set of k polygons with a total of n vertices moving along bounded degree algebraic motions, this dual diagram, and thus their compact Voronoi diagram, changes combinatorially Ω(n2) and O(kn2β(k)β(n)) times, where β(ċ) is an extremely slowly growing function. This compact Voronoi diagram can be used for collision detection or retraction motion planning among the moving polygons.
9735559
Probabilistic analysis for combinatorial functions of moving points
We initiate a probabilistic study of configuration functions of moving points. In our probabilistic model, a particle is given an initiaf position and a velocity drawn independently at random from the same distribution D. We show that if n particles are drawn independently at random from the uniform distribution on the square, their convex hull undergoes El(logz n) combinatorial changes in expectation, their Voronoi diagram undergoes e(n312 ) combinatorial changes, and their closest pair undergoes El(n) combinatorial changes.
11411902
Kinetic connectivity for unit disks
We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unit-radius disks moving in the plane. We assume that the motion of each disk can be specified by a low-degree algebraic trajectory; this trajectory, however, can be modified in an on-line fashion. While the disks move continuously, their connectivity changes at discrete times. Our main result is an O(n) space data structure that takes O(log n\slash \kern -1pt log log n) time per connectivity query of the form ``are disks A and B in the same connected component?’’ A straightforward approach based on dynamically maintaining the overlap graph requires Ω (n 2 ) space. Our data structure requires only linear space and must deal with O(n 2 + e ) updates in the worst case, each requiring O(log 2 n) amortized time, for any e>0 . This number of updates is close to optimal, since a set of n moving unit disks can undergo Ω (n 2 ) connectivity changes.
15420689
Similarity space projection for web image search and annotation
Web image search has been explored and developed in academic as well as commercial areas for over a decade. To measure the similarity between Web images and user queries, most of the existing Web image search systems try to convert an image to textual keywords by analyzing the textual information available (such as surrounding text and image filename) with or without leveraging image visual features (such as color, texture, shape). In this way, the existing systems transform "Web images" to the "query (text)" space so as to compare the relevance of images to the query. In this paper, we present a novel solution to Web image search - similarity space projection (SSP). This algorithm takes images and queries as two heterogeneous object peers, and projects them into a third Euclidean "similarity space" in which their similarity can be directly measured. The rule of projection guarantees that in the new space the relevant images are kept close to the corresponding query and those irrelevant ones are away from it. Experiments on real-world Web image collections showed that the proposed algorithm significantly outperformed traditional information retrieval models (such as vector space model) in the application of image search. Besides Web image search, we demonstrate that this algorithm can also be applied to image annotation scenario, and has promising performance. Thus, this algorithm unifies Web image search and image annotation into same framework.
627898
Fault-tolerant data delivery for multicast overlay networks
Overlay networks represent an emerging technology for rapid deployment of novel network services and applications. However, since public overlay networks are built out of loosely coupled end-hosts, individual nodes are less trustworthy than Internet routers in carrying out the data forwarding function. Here we describe a set of mechanisms designed to detect and repair errors in the data stream. Utilizing the highly redundant connectivity in overlay networks, our design splits each data stream to multiple sub-streams which are delivered over disjoint paths. Each sub-stream carries additional information that enables receivers to detect damaged or lost packets. Furthermore, each node can verify the validity of data by periodically exchanging Bloom filters, the digests of recently received packets, with other nodes in the overlay. We have evaluated our design through both simulations and experiments over a network testbed. The results show that most nodes can effectively detect corrupted data streams even in the presence of multiple tampering nodes.
205876162
Independence and connectivity in 3-domination-critical graphs
Let δ, γ, κ and α be, respectively, the minimum degree, the domination number, the con nectivity and the independence number of a graph G. The graph G is 3-domination-critical if γ = 3 and the addition of any edge decreases γ by 1. In this paper, we prove that if G is a 3-domination-critical graph, then α ≤ κ + 2; and moreover, if κ ≤ δ -1, then α ≤ κ + 1. We also give a short proof of Wojcicka's result, which says that every connected 3-domination-critical graph of order at least 7 contains a hamiltonian path (J. Graph Theory 14 (1990) 205).
14199573
Zapato: Automatic Theorem Proving for Predicate Abstraction Refinement
Counterexample-driven abstraction refinement is an automatic process that produces abstract models of finite and infinite-state systems. When this process is applied to software, an automatic theorem prover for quantifier-free first-order logic helps to determine the feasibility of program paths and to refine the abstraction. In this paper we report on a fast, lightweight, and automatic theorem prover called Zapato which we have built specifically to solve the queries produced during the abstraction refinement process.
17414114
On the application of cross correlation function to subsample discrete time delay estimation
Cross correlation function (CCF) of signals is an important tool of multi-sensors signal processing. Parabola functions are commonly used as parametric models of the CCF in time delay estimation. The parameters are determined by fitting samples near the maximum of the CCF to a parabola function. In this paper we analyze the CCF for the stationary processes of exponential auto-correlation function, with respect to two important types of sensor sampling kernels. Our analysis explains why the parabola is an acceptable model of CCF in estimating the time delay. More importantly, we demonstrate that the Gaussian function is a better and more robust approximation of CCF than the parabola. This new approximation approach leads to higher precision in time delay estimation using the CCF peak locating strategy. Simulations are also carried out to evaluate the performance of the proposed estimation method for different sample window sizes and signal to noise ratios. The new method offers significant improvement over the current parabola based method.