19187096
Traveling salesman problem of segments
In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n ∊-separated segments in two dimensional space. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique5 for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n2(log n)O(1/∊2)) time to compute a (1+∊)-approximation with probability ≥l/2, and can be derandomized with an additional factor of O(n2).
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.
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.
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.
29728094
Graph Bandwidth of Weighted Caterpillars
Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars and general graphs. More specifically, we show that the GBM problem on caterpillars with hair-length at most 2 and the GBM problem on star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log(nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum wedge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm and some experimental results. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of c log(n) of the lower bound for a small number c, which is consistent with the inapproximability results of this problem (i.e., no constant approximation for the GBM problem unless P = NP). © 2006 Published by Elsevier B.V.
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.
53246204
Design of a high-performance ATM firewall
A router-based packet-filtering firewall is an effective way of protecting an enterprise network from unauthorized access. However, it will not work efficiently in an ATM network because it requires the termination of end-to-end ATM connections at a packet-filtering router, which incurs huge overhead of SAR (Segmentation and Reassembly). Very few approaches to this problem have been proposed in the literature, and none is completely satisfactory. In this paper we present the hardware design of a high-speed ATM firewall that does not require the termination of an end-to-end connection in the middle. We propose a novel firewall design philosophy, called Quality of Firewalling (QoF), that applies security measures of different strength to traffic with different risk levels and show how it can be implemented in our firewall. Compared with the traditional firewalls, this ATM firewall performs exactly the same packet-level filtering without compromising the performance and has the same "look and feel" by sitting at the chokepoint between the trusted ATM LAN and untrusted ATM WAN. It is also easy to manage and flexible to use.
240982
Data streaming algorithms for estimating entropy of network traffic
Using entropy of traffic distributions has been shown to aid a wide variety of network monitoring applications such as anomaly detection, clustering to reveal interesting patterns, and traffic classification. However, realizing this potential benefit in practice requires accurate algorithms that can operate on high-speed links, with low CPU and memory requirements. In this paper, we investigate the problem of estimating the entropy in a streaming computation model. We give lower bounds for this problem, showing that neither approximation nor randomization alone will let us compute the entropy efficiently. We present two algorithms for randomly approximating the entropy in a time and space efficient manner, applicable for use on very high speed (greater than OC-48) links. The first algorithm for entropy estimation is inspired by the structural similarity with the seminal work of Alon et al. for estimating frequency moments, and we provide strong theoretical guarantees on the error and resource usage. Our second algorithm utilizes the observation that the performance of the streaming algorithm can be enhanced by separating the high-frequency items (or elephants) from the low-frequency items (or mice). We evaluate our algorithms on traffic traces from different deployment scenarios.
11752783
Design of a high-performance ATM firewall
A router-based packet-filtering firewall is an effective way of protecting an enterprise network from unauthorized access. However, it will not work efficiently in an ATM network because it requires the termination of end-to-end ATM connections at a packet-filtering router, which incurs huge overhead of SAR (Segmentation and Reassembly). Very few approaches to this problem have been proposed in the literature, and none is completely satisfactory. In this paper we present the hardware design of a high-speed ATM firewall that does not require the termination of an end-to-end connection in the middle. We propose a novel firewall design philosophy, called Quality of Firewalling (QoF), that applies security measures of different strength to traffic with different risk levels and show how it can be implemented in our firewall. Compared with the traditional firewalls, this ATM firewall performs exactly the same packet-level filtering without compromising the performance and has the same “look and feel” by sitting at the chokepoint between the trusted ATM LAN and untrusted ATM WAN. It is also easy to manage and flexible to use.
17405074
Extracting Meaningful Entities from Police Narrative Reports
Valuable criminal-justice data in free texts such as police narrative reports are currently difficult to be accessed and used by intelligence investigators in crime analyses. It would be desirable to automatically identify from text reports meaningful entities, such as person names, addresses, narcotic drugs, or vehicle names to facilitate crime investigation. In this paper, we report our work on a neural network-based entity extractor, which applies named-entity extraction techniques to identify useful entities from police narrative reports. Preliminary evaluation results demonstrated that our approach is feasible and has some potential values for real-life applications. Our system achieved encouraging precision and recall rates for person names and narcotic drugs, but did not perform well for addresses and personal properties. Our future work includes conducting larger-scale evaluation studies and enhancing the system to capture human knowledge interactively.
11532584
Sequentially t-Diagnosable Systems: A Characterization and Its Applications
In the system level fault diagnosis area, the fundamental problem of characterizing sequentially t-diagnosable systems in the PMC model has remained open for more than two decades. We resolve this problem by providing a complete characterization of such systems. Our solution to the characterization problem leads to the correct identification of optimal sequentially t-diagnosable D/sub /spl delta/,k/ systems. Given a set of n units where n=2t+1, an optimal D/sub /spl delta/,k/ system can be constructed with just n([(t+2)/3]) tests, rather than n([t/2]+1) tests-a previously misjudged bound. An efficient algorithm for identifying the set of faulty units in a sequentially t-diagnosable D/sub /spl delta/,k/ system is given along the line of the proposed characterization, which is linear with respect to the number of tests in the system. >