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.
27008432
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 Ɛ-separated segments in two dimensional space. Our results are based on a number of geometric observations and an interesting generalization of Arora's technique [5] for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n2(log n)O(1/Ɛ4)) time to compute a (1 + Ɛ)-approximation with probability ≥ 1/2, and can be derandomized with an additional factor of O(n2). Our technique is likely applicable to TSP problems of certain Jordan arcs and related problems.
17909513
Determining an optimal penetration among weighted regions in two and three dimensions
We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.
52802993
Issues and challenges in the performance analysis of real disk arrays
The performance modeling and analysis of disk arrays is challenging due to the presence of multiple disks, large array caches, and sophisticated array controllers. Moreover, storage manufacturers may not reveal the internal algorithms implemented in their devices, so real disk arrays are effectively black-boxes. We use standard performance techniques to develop an integrated performance model that incorporates some of the complexities of real disk arrays. We show how measurement data and baseline performance models can be used to extract information about the various features implemented in a disk array. In this process, we identify areas for future research in the performance analysis of real disk arrays.
16352747
Defeating memory corruption attacks via pointer taintedness detection
Most malicious attacks compromise system security through memory corruption exploits. Recently proposed techniques attempt to defeat these attacks by protecting program control data. We have constructed a new class of attacks that can compromise network applications without tampering with any control data. These non-control data attacks represent a new challenge to system security. In this paper, we propose an architectural technique to defeat both control data and non-control data attacks based on the notion of pointer taintedness. A pointer is said to be tainted if user input can be used as the pointer value. A security attack is detected whenever a tainted value is dereferenced during program execution. The proposed architecture is implemented on the SimpleScalar processor simulator and is evaluated using synthetic programs as well as real-world network applications. Our technique can effectively detect both control data and non-control data attacks, and it offers better security coverage than current methods. The proposed architecture is transparent to existing programs.
11854232
Local and parallel finite element algorithms based on two-grid discretizations
A number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a ne grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for nite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory. In this paper, we will propose some new parallel techniques for nite element computation. These techniques are based on our understanding of the local and global properties of a nite element solution to some elliptic problems. Simply speaking, the global behavior of a solution is mostly governed by low frequency components while the local behavior is mostly governed by high frequency compo- nents. The main idea of our new algorithms is to use a coarse grid to approximate the low frequencies and then to use a ne grid to correct the resulted residue (which contains mostly high frequencies) by some local/parallel procedures. Let us now give a somewhat more detailed but informal (and hopefully infor- mative) description of the main ideas and results in this paper. We consider the following very simple model problem posed on a convex polygonal domain R 2 : ( u + bru = f; in ;
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.
6883771
A firewalling scheme for securing MPOA-based enterprise networks
A well-known security problem with MPOA is that cut-through connections generally bypass firewall routers if there are any. None of the previously proposed approaches solved the problem properly. We propose a novel firewalling scheme for MPOA that nicely fixes the security hole. Our firewalling scheme has three outstanding advantages that make it ideal for securing MPOA-based enterprise networks. First, based on our novel concept of logical chokepoints, our firewalling scheme does not require the existence of physical chokepoints inside the network. Second, the scheme is nicely embedded into the MPOA protocol so that its cost, performance overhead, and protocol complexity are reduced to a minimum. Third, the scheme is centrally administrated so that it scales well to very large networks.