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1.
Depending on whether bidirectional links or unidirectional links are used for communications, the network topology under a
given range assignment is either an undirected graph referred to as the bidirectional topology, or a directed graph referred
to as the unidirectional topology. The Min-Power Bidirectional (resp., Unidirectional) k-Node Connectivity problem seeks a range assignment of minimum total power subject to the constraint that the produced bidirectional
(resp. unidirectional) topology is k-vertex connected. Similarly, the Min-Power Bidirectional (resp., Unidirectional) k-Edge Connectivity problem seeks a range assignment of minimum total power subject to the constraint the produced bidirectional
(resp., unidirectional) topology is k-edge connected.
The Min-Power Bidirectional Biconnectivity problem and the Min-Power Bidirectional Edge-Biconnectivity problem have been studied
by Lloyd et al. [23]. They show that range assignment based the approximation algorithm of Khuller and Raghavachari [18],
which we refer to as Algorithm KR, has an approximation ratio of at most 2(2 – 2/n)(2 + 1/n) for Min-Power Bidirectional Biconnectivity, and range assignment based on the approximation algorithm of Khuller and Vishkin [19],
which we refer to as Algorithm KV, has an approximation ratio of at most 8(1 – 1/n) for Min-Power Bidirectional Edge-Biconnectivity.
In this paper, we first establish the NP-hardness of Min-Power Bidirectional (Edge-) Biconnectivity. Then we show that Algorithm KR has an approximation ratio of at most 4 for both Min-Power Bidirectional Biconnectivity and Min-Power Unidirectional Biconnectivity,
and Algorithm KV has an approximation ratio of at most 2k for both Min-Power Bidirectional k-Edge Connectivity and Min-Power Unidirectional k-Edge Connectivity. We also propose a new simple constant-approximation algorithm for both Min-Power Bidirectional Biconnectivity
and Min-Power Unidirectional Biconnectivity. This new algorithm applies only to Euclidean instances, but is best suited for
distributed implementation.
A preliminary version of this work appeared in the proceedings of the 2nd International Conference on AD-HOC Network and Wireless
(Adhoc-Now 2003).
Research performed in part while visiting the Max-Plank-Institut fur Informatik.
Gruia Calinescu is an Assistant Professor of Computer Science at the Illinois Institute of Technology since 2000. He held postdoc or visiting
researcher positions at DIMACS, University of Waterloo, and Max-Plank Institut fur Informatik. Gruia has a Diploma from University
of Bucharest and a Ph.D. from Georgia Insitute of Technology. His research interests are in the area of algorithms.
Peng-Jun Wan has joined the Computer Science Department at Illinois Institute of Technology in 1997 and has been an Associate Professor
since 2004. He received his Ph.D. in Computer Science from University of Minnesota in 1997, M.S. in Operations Research and
Control Theory from Chinese Academy of Science in 1993, and B.S. in Applied Mathematics from Tsinghua University in 1990.
His research interests include optical networks and wireless networks. 相似文献
2.
3.
Javier Ramírez Antonio García Uwe Meyer-Bäse Fred Taylor Antonio Lloris 《The Journal of VLSI Signal Processing》2003,33(1-2):171-190
Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength). 相似文献
4.
5.
We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch. 相似文献
6.
随着电容测量技术的迅速发展,电容传感器在非电量测量和自动检测中得到广泛应用,但它在使用过程中也存在一些问题,针对在使用电容传感器过程中存在的几个问题,从电容传感器的原理和工作过程两个方面进行了讨论,并提出行之有效的处理方法。 相似文献
7.
We provide a rigorous derivation of an asymptotic formula for perturbations in the eigenvalues caused by the presence of a finite number of inhomogeneities of small diameter with conductivity different from the background conductivity. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
8.
A. B. Vasil’eva A. A. Plotnikov 《Computational Mathematics and Mathematical Physics》2006,46(5):762-767
A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed. 相似文献
9.
A. Ulyanenkov 《Applied Surface Science》2006,253(1):106-111
Several novel methods for evaluation and interpretation of X-ray data from modern nanostructures are presented along with their applications. The background of methods and their relations to fundamental problems of X-ray analysis is shortly described. The key features of LEPTOS software, which is designed for the analysis of X-ray data measured with various geometries and setups and implements all discussed techniques, are discussed. 相似文献
10.
This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献