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.
15556637
Proximity problems on moving points
A kinetic data structure for the maintenance of a multidimensional range search tree is introduced. This structure is used as a building block to obtain kinetic data structures for two classical geometric proximity problems in arbitrary dlmensions: the first structure maintains the closest pair of a set of continuously moving points, and is provably efficient. The second structure maintains a spanning tree of the moving points whose cost remains within some prescribed factor of the minimum spanning tree.
100573
A hierarchical method for real-time distance computation among moving convex bodies
Abstract 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 Dobkin–Kirkpatrick 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 and provides consistent performance.
11907465
Deformable Free-Space Tilings for Kinetic Collision Detection†
We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously. Unlike classical collision detection methods that rely on bounding volume hierarchies, our method is based on deformable tilings of the free space surrounding the polygons. The basic shape of our tiles is that of a pseudo-triangle, a shape sufficiently flexible to allow extensive deformation, yet structured enough to make detection of self-collisions easy. We show different schemes for maintaining pseudo-triangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that the pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. In addition, by refining the pseudo-triangulation, we show triangulations of points that only change about O(n 7 / 3 ) times for linear motion. We then describe an algorithm for maintaining a pseudo-triangulation of a set of convex polygons. Finally, we extend our algorithm to the general case of maintaining a pseudo-triangulation of a set of moving or deforming simple polygons.
9035359
Visibility Queries in Simple Polygons and Applications
In this paper we explore some novel aspects of visibility for stationary and moving points inside a simple polygon P. We provide a mechanism for expressing the visibility polygon from a point as the disjoint union of logarithmically many canonical pieces using a quadraticspace data structure. This allows us to report visibility polygons in time proportional to their size, but without the cubic space overhead of earlier methods. The same canonical decomposition can be used to determine visibility within a frustum, or to compute various attributes of the visibility polygon efficiently. By exploring the connection between visibility polygons and shortest path trees, we obtain a kinetic algorithm that can track the visibility polygon as the viewpoint moves along polygonal paths inside P, at a polylogarithmic cost per combinatorial change in the visibility. The combination of the static and kinetic algorithms leads to a space query-time tradeoff for the visibility from a point problem and an output-sensitive algorithm for the weak visibility from a segment problem.
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.
7255987
Relationship between support vector set and kernel functions in SVM
Based on a constructive learning approach, covering algorithms, we investigate the relationship between support vector sets and kernel functions in support vector machines (SVM). An interesting result is obtained. That is, in the linearly non-separable case, any sample of a given sample setK can become a support vector under a certain kernel function. The result shows that when the sample setK is linearly non-separable, although the chosen kernel function satisfies Mercer’s condition its corresponding support vector set is not necessarily the subset ofK that plays a crucial role in classifyingK. For a given sample set, what is the subset that plays the crucial role in classification? In order to explore the problem, a new concept, boundary or boundary points, is defined and its properties are discussed. Given a sample setK, we show that the decision functions for classifying the boundary points ofK are the same as that for classifying theK itself. And the boundary points ofK only depend onK and the structure of the space at whichK is located and independent of the chosen approach for finding the boundary. Therefore, the boundary point set may become the subset ofK that plays a crucial role in classification. These results are of importance to understand the principle of the support vector machine (SVM) and to develop new learning algorithms.
15884973
Applications of SAT Solvers to Cryptanalysis of Hash Functions
Several standard cryptographic hash functions were broken in 2005. Some essential building blocks of these attacks lend themselves well to automation by encoding them as CNF formulas, which are within reach of modern SAT solvers. In this paper we demonstrate effectiveness of this approach. In particular, we are able to generate full collisions for MD4 and MD5 given only the differential path and applying a (minimally modified) off-the-shelf SAT solver. To the best of our knowledge, this is the first example of a SAT-solver-aided cryptanalysis of a non-trivial cryptographic primitive. We expect SAT solvers to find new applications as a validation and testing tool of practicing cryptanalysts.
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.
18035076
On Subsumption Removal and On-the-Fly CNF Simplification
CNF Boolean formulas generated from resolution or solution enumeration often have much redundancy. Efficient algorithms are needed to simplify and compact such CNF formulas. In this paper, we present a novel algorithm to maintain a subsumption-free CNF clause database by efficiently detecting and removing subsumption as the clauses are being added. We then present an algorithm that compact CNF formula further by applying resolutions to make it Decremental Resolution Free. Our experimental evaluations show that these algorithms are efficient and effective in practice.
46136838
IPv6 traffic with multi-class QoS in VPN
Abstract This paper focuses on the modeling and performance analysis for IPv6 traffic with multi-class QoS in virtual private networks (VPNs). The multi-class QoS is implemented on differentiated service basis using priority scheme of 4 bits defined in the packet header of IPv6. A VPN-enabled IP router is modeled as a tandem queuing system in which each output link consists of two parallel priority output queues. The high-priority queue is used to carry the delay sensitive traffic while the low-priority queue is used to carry the delay insensitive traffic. On the other hand, multiple thresholds are implemented in each queue, respectively, for packet loss priority control. The performance analysis is done using fluid flow techniques. The numerical results obtained from the analysis show that the differentiated service based on the priority schemes defined in IPv6 is able to effectively satisfy the multi-class QoS requirement for supporting multimedia services in VPN. The performance trade-off between the delay sensitive traffic and delay insensitive traffic in terms of traffic throughput, packet loss probability and end-to-end delay in VPN networks is presented.