Tsan-sheng Hsu. Graph Augmentation and Related Problems: Theory and Practice. Ph.d. thesis, University of Texas at Austin, January 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as good as guaranteed by using totally random bits. Karlo and Raghavan [KR93] assumed the same model and showed that Quicksort can have much poorer performance than predicted. Other peculiarities of certain pseudo random functions were noted in [FLW92] for Monte Carlo simulations and in [HR96, Hsu97] for parallel implementations of basic graph algorithms. Although debunking commonly used pseudo random functions is worthwhile, the lesson here is to design algorithms which demand much less randomness, and more important, to analyze them in a realistic abstract environment. There has been ....

Tsan-sheng Hsu. Graph Augmentation and Related Problems: Theory and Practice. Ph.d. thesis, University of Texas at Austin, January 1997.

....algorithms. In practice, programs get their random bits by using pseudo random number generators. Yet even in practice there are reports of algorithms giving quite different results under different pseudo random generators; see, e.g. FLW] for such reports on Monte Carlo simulations, and [Hsu, HRD] for the deviant performance of some RNC algorithms for graph problems. Other approaches involve using a physical source of randomness, such as a Zener diode, or using the last digits of a real time clock. Not only is it not clear that such Part of this work was done while the authors attended ....

T.-s. Hsu, Graph Augmentation and Related Problems: Theory and Practice, PhD thesis, Department of Computer Sciences, University of Texas at Austin, October 1993.

....get their random bits by using pseudo random number generators. Empirically, this often seems to be sufficient. However, there are reports of algorithms giving quite different results under different pseudo random generators (see e.g. FLW92] for such reports on Monte Carlo simulations, and [Hsu93, HRD94] for the deviant performance of some RNC algorithms for graph problems) An alternative approach is to use the output of some physical source of randomness, such 48 as a Zener diode, or the last digits of a real time clock. For such a source, it is plausible to assume that the string of bits ....

T.-s. Hsu. Graph augmentation and related problems: theory and practice. PhD thesis, Department of Computer Sciences, University of Texas at Austin, October 1993.

.... high [17] There have also been reports of Monte Carlo simulations giving quite different results under different random number generators [12] and direct implementations of certain RNC algorithms taking longer time than expected due to the pseudorandom nature of computer generated random bits [15, 14]. In this paper, we present two new techniques for derandomization. The first leads to improved NC algorithms for many basic problems such as finding large cuts in graphs, set discrepancy, Delta 1) vertex coloring of graphs and others while the second improves the constructions due to [11] of ....

T.-s. Hsu, Graph augmentation and related problems: theory and practice, PhD thesis, Department of Computer Sciences, University of Texas at Austin, October 1993.

....For more information on such problems see recent papers by Frank [10] and Naor, Gusfield and Martel [32] For the vertex connectivity case, the problem appears to be significantly harder and no polynomial time algorithm is known for finding the optimal solution. In his doctoral thesis, Hsu [22] gives algorithms for vertex connectivity for small connectivity values. These algorithms are quite complex. It must be pointed out that the problem of constructing a graph with n vertices, and connectivity with the least number of edges was first addressed by Harary [19] The first paper to ....

T. S. Hsu, Graph Augmentation and Related Problems: Theory and Practice, Ph. D thesis, Dept. of Computer Science, University of Texas, Austin, TX (1993).

....get their random bits by using pseudo random number generators. Empirically, this often seems to be sufficient. However, there are reports of algorithms giving quite different results under different pseudo random generators (see e.g. FLW92] for such reports on Monte Carlo simulations, and [Hsu93, HRD94] for the deviant performance of some RNC algorithms for graph problems) An alternative approach is to use the output of some physical source of randomness, such as a Zener diode, or the last digits of a real time clock. For such a source, it is plausible to assume that the string of bits output ....

T.-s. Hsu, "Graph augmentation and related problems: theory and practice," PhD thesis, Department of Computer Sciences, University of Texas at Austin, October 1993.

....systematic description of the above information is the structure of the graph with respect to its vertex connectivity. Knowing the structure of a graph can lead to the solution of important graph theoretical problems such as the augmentation problem that is studied here (see the survey chapter in [Hsu93]) and dynamic graph algorithms [LP91] The structure of an undirected graph that is not biconnected (i.e. 2 vertex connected) is well known [Har69] and is represented as a 2 block graph. The structure of a biconnected graph that is not triconnected (i.e. 3 vertex connected) is also well known ....

....the smallest four connectivity augmentation number and for finding such a smallest four connectivity augmentation. Finally, we give concluding remarks in Section 9. 2 Related Work We give a brief summary of related work in this section. More details can be found in the survey chapter in [Hsu93]. 3 2.1 Vertex Connectivity Augmentation The following results are known for solving the smallest augmentation problem on an undirected graph to satisfy a given vertex connectivity requirement. Eswaran and Tarjan [ET76] and Plesn ik [Ple76] independently) gave a lower bound for the ....

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T.-s. Hsu. Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin, October 1993.

....Carolina 27706, USA. E mail: kao cs.duke.edu. Research supported in part by NSF Grant CCR 9101385. drawing planar graphs nicely [14] This problem has been extensively studied for the cases of making a whole graph k edge connected or k vertex connected for various values of k (see the survey in [9]) Recently, there have been studies on how to make only a given vertex subset satisfy a connectivity requirement [4, 25, 28, 29, 30] This generalization of the smallest augmentation problem arises naturally from practical applications. For example, in the case of improving network reliability, a ....

T.-s. Hsu. Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin, October 1993.

....1 Supported by NSF Grant CCR 90 23059 and Texas Advanced Research Projects Grant 003658480. A preliminary version of this paper appears in Proceedings of the Seventh IEEE Symposium on Parallel and Distributed Processing, 1995, pp. 154 159. This work is also reported in T. s. Hsu s Ph.D. thesis [18]. 2 Also supported by an IBM graduate fellowship. Part of this work was done while this author was with Department of Computer Sciences, University of Texas at Austin. 3 Also supported by Texas Advanced Research Projects Grant 0003658386. 2 High Level Description of Our Implementation We ....

T.-s. Hsu. Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin, October 1993.

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