33666708
Topological Peeling and Applications
We present a new approach, called topological peeling, for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walk may not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walk by 10–25% in execution time.
28240465
Motion Tracking and Intensity Surface Recovery in Microscopic Nuclear Images
Current techniques for microscopic imaging do not provide necessary spatial and temporal resolutions for real time visualization of the nucleus. Images can only be acquired in time lapse mode, leading to significant loss of information between image frames. Such data, if available, can be extremely helpful in the study of nuclear organization and function. In this paper, we present a gamut of geometric-technique-based approaches for solving the problem. Our techniques, working together, can effectively recover complicated motion and deformation as well as the change of intensity surfaces from pairs of images in a microscopic image sequence, and has low time complexity, particularly desirable by many biological applications where large amount of DNA need to be processed. These techniques are also readily applicable to other types of images for reconstructing motion and intensity surfaces of deformable objects.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
5727433
An Experimental Study and Comparison of Topological Peeling and Topological Walk
In this paper, we present an experimental study comparing two algorithms, topological peeling and topological walk, for traversing arrangements of planar lines. Given a set H of n lines and a convex region R on a plane, both topological peeling and topological walk sweep the portion AR of the arrangement of H inside R in O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells of AR and r is the number of boundary vertices of R. In our study, we robustly implemented these two algorithms using the LEDA library. Based on the implementation, we carried out experiments to conduct several comparisons, such as the arrangement traversal fashions, memory consumption, and execution time. In general, topological peeling exhibits a better control on the propagation of its sweeping curve (called the wavefront). For memory consumption, two types of measures, logical and physical memory, were examined. Our experiments showed that although both algorithms use nearly the same amount of logical memory, topological peeling could use twice as much physical memory as topological walk. For execution time, experiments revealed an interesting phenomenon that topological peeling has a 10% to 25% faster execution time than topological walk in most cases. Our analysis of this phenomenon indicates that the execution times of topological peeling and topological walk are both sensitive to the ratio of the lower input lines to all input lines. When the ratio of the lower lines to all input lines is around 85%, the two algorithms have roughly the same amount of execution time. Under this ratio, topological peeling considerably outperforms topological walk; above this ratio, topological walk slightly outperforms topological peeling.
42016450
Geometric permutations of higher dimensional spheres
In this paper, we prove that the maximum number of geometric permutations (induced by line transversals) of a set of n pairwise disjoint spheres with a bounded radius ratio in Rd for d ≥ 3 is at most 2⌊√2M⌋+1, where M is the ratio of the largest radius and the smallest radius of the spheres. Setting M to 1, this gives an upper bound of 4 on the maximum number of geometric permutations for congruent spheres in Rd, matching a recently independently discovered result [Y. Zhou, S. Suri, in: Proc. of 12th Annual ACM-SIAM Symp. on Discrete Algorithms, 2001, pp. 234-243] on this case. Our result settles a conjecture in combinatorial geometry.
21098955
Topological Peeling and Implementation
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walkb y 10 - 15% in execution time.
11266138
Proxy cache management for fine-grained scalable video streaming
Caching video objects at proxies close to clients has attracted a lot of attention in recent years. To meet diverse client bandwidth conditions, there have been research efforts to combine proxy caching with video layering or transcoding. Nevertheless, these adaptive systems suffer from either coarse adaptation granularity due to the inflexible structures of existing layered coders or high computation overhead due to the transcoding operations. In this paper, we propose a novel adaptive video caching framework that enables low-cost and fine-grained adaptation. The innovative approach employs the MPEG-4 fine-grained scalable (FGS) video with postencoding rate control. We demonstrate that the proposed framework is both network aware and media adaptive: clients can be of heterogeneous streaming rates, and the backbone bandwidth consumption can be adaptively controlled. We also examine the design and management issues in the framework, in particular, the optimal stream portions to cache and the optimal streaming rate to each client. Simulation results demonstrate that, compared to nonadaptive caching, the proposed framework with optimal cache management not only achieves significant reduction on transmission costs but also enables flexible utility assignment for the heterogeneous clients. Meanwhile, its computational overhead is kept at a low level, implying that it is practically deployable
15892344
Design of a novel statistics counter architecture with optimal space and time efficiency
The problem of how to efficiently maintain a large number (say millions) of statistics counters that need to be incremented at very high speed has received considerable research attention recently. This problem arises in a variety of router management algorithms and data streaming algorithms, where a large array of counters is used to track various network statistics and to implement various counting sketches respectively. While fitting these counters entirely in SRAM meets the access speed requirement, a large amount of SRAM may be needed with a typical counter size of 32 or 64 bits, and hence the high cost. Solutions proposed in recent works have used hybrid architectures where small counters in SRAM are incremented at high speed, and occasionally written back ("flushed") to larger counters in DRAM. Previous solutions have used complex schedulers with tree-like or heap data structures to pick which counters in SRAM are about to overflow, and flush them to the corresponding DRAM counters.In this work, we present a novel hybrid SRAM/DRAM counter architecture that consumes much less SRAM and has a much simpler design of the scheduler than previous approaches. We show, in fact, that our design is optimal in the sense that for a given speed difference between SRAM and DRAM, our design uses the theoretically minimum number of bits per counter in SRAM. Our design uses a small write-back buffer (in SRAM) that stores indices of the overflowed counters (to be flushed to DRAM) and an extremely simple randomized algorithm to statistically guarantee that SRAM counters do not overflow in bursts large enough to fill up the write-back buffer even in the worst case. The statistical guarantee of the algorithm is proven using a combination of worst case analysis for characterizing the worst case counter increment sequence and a new tail bound theorem for bounding the probability of filling up the write-back buffer. Experiments with real Internet traffic traces show that the buffer size required in practice is significantly smaller than needed in the worst case.
8292124
Effective retrieval with distributed collections
Abstract : This paper evaluates the retrieval effectiveness of distributed information retrieval systems in realistic environments. We find that when a large number of collections are available, the retrieval effectiveness is significantly worse than that of centralized systems, mainly because typical queries are not adequate for the purpose of choosing the right collections. We propose two techniques to address the problem. One is to use phrase information in the collection selection index and the other is query expansion. Both techniques enhance the discriminatory power of typical queries for choosing the right collections and hence significantly improve retrieval results. Query expansion, in particular, brings the effectiveness of searching a large set of distributed collections close to that of searching a centralized collection.
2460253
Approximate processing of massive continuous quantile queries over high-speed data streams
Quantile computation has many applications including data mining and financial data analysis. It has been shown that an /spl epsi/-approximate summary can be maintained so that, given a quantile query (/spl phi/,/spl epsi/), the data item at rank /spl lceil//spl phi/N/spl rceil/ may be approximately obtained within the rank error precision /spl epsi/N over all N data items in a data stream or in a sliding window. However, scalable online processing of massive continuous quantile queries with different /spl phi/ and /spl epsi/ poses a new challenge because the summary is continuously updated with new arrivals of data items. In this paper, first we aim to dramatically reduce the number of distinct query results by grouping a set of different queries into a cluster so that they can be processed virtually as a single query while the precision requirements from users can be retained. Second, we aim to minimize the total query processing costs. Efficient algorithms are developed to minimize the total number of times for reprocessing clusters and to produce the minimum number of clusters, respectively. The techniques are extended to maintain near-optimal clustering when queries are registered and removed in an arbitrary fashion against whole data streams or sliding windows. In addition to theoretical analysis, our performance study indicates that the proposed techniques are indeed scalable with respect to the number of input queries as well as the number of items and the item arrival rate in a data stream.
789303
DNA Sequence Design Based on Template Strategy
In DNA based computation and DNA nanotechnology, the design of proper DNA sequences has turned out to be an elementary problem. This paper takes a further look at the template strategy proposed in work by Frutos, A. G. et al. (Nucleic Acids Res. 1997, 25, 4748-4757). The H-measure proposed by Garzon et al. (Proceedings of the Second Annual Genetic Programming Conference, 1997; pp 472-487) is combined in this strategy to optimize the template and map sets obtained. Finally we describe a constructing method that can still produce more sequences by the results obtained in this paper.