J. Berry and M. Goldberg. Path optimization for graph partitioning problem. Discrete Applied Mathematics, 90:27--50, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in the unit square and whose edges between any pair of nodes exist when their distance is smaller than some parameter r n . Random geometric graphs have been proposed as a possible model to take into account the structural characteristics of instances that appear in many practical applications [8, 55, 65]. Random geometric graphs also exhibit a phase transition [85] When nr 2 n # # there exists a critical parameter # c such that if # # c , graphs G(n; r n ) are likely to have O(log n) points in each connected component, while if # # c , there is likely to be a component with #(n) ....

J. W. Berry and M. K. Goldberg. Path Optimization for Graph Partitioning Problems. Technical report TR: 95-34, DIMACS, 1995.

....[0, 1] 2 . For any natural n, we write X n = X 1 , X n and denote by G(X n ; r n ) the random geometric graph of n nodes on X n and radius r n . Many empirical studies have used random geometric graphs as a basis to benchmark heuristics for layout or partitioning problems [16, 4, 21, 31]; however, their theoretical study is still incipient (see [11] for a survey) Similarly to site percolation, continuum percolation and random geometric graphs exhibit a phase transition [29] Suppose lim n ## nr 2 n = #; then there exists a critical parameter # c such that when # # c , ....

J. W. Berry and M. K. Goldberg. Path optimization for graph partitioning problems. Discrete Applied Mathematics. Combinatorial Algorithms, Optimization and Computer Science, 90(1-3):27--50, 1999.

....are graphs whose n vertices are n points uniformly distributed in the unit square and whose edges between any pair of distinct nodes exist when their distance is smaller than some parameter r. Many empirical studies have used random models of geometric graphs for layout or partitioning problems [39, 7, 49, 67]. However, the theoretical study of random geometric graphs has been mainly focused on parameters as their clique or chromatic number and their connectivity properties (see [22] for a survey) Therefore, the analysis of layout measures in random geometric graphs certainly seems worthwhile to ....

....geometric graphs. The problem of partitioning a graph into a number of pieces is a fundamental task in computer science. Many heuristics have been proposed for these problems and many libraries implement them. On the other hand, the bisection of geometric random graphs has already been considered [39, 7, 49]. In the following, we analyze the behavior of the Projection algorithm and of several heuristics included in the Chaco and Party libraries [36, 68] for the EdgeBis problem on random geometric graphs with r = # log 2 n n. These libraries o#er global and local heuristics which can be combined. ....

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J. W. Berry and M. K. Goldberg. Path optimization for graph partitioning problems. Discrete Applied Mathematics. Combinatorial Algorithms, Optimization and Computer Science, 90(1-3):27--50, 1999.

....design such as logic partitioning [12] and placement [6, 19] Because of these applications, the GPP has been used as a testing ground for many heuristics. For our work, a selection had to be made; in view of the previous studies by Johnson et al. 13] Lang and Rao [20] and Berry and Goldberg [4], we have restricted our study to iterative improvement heuristics based on local search and to simulated annealing. Having made a choice of optimization problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the ....

....problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the structure of the actual instances of interest to the practitioner. Since we do not have a particular application in mind, we shall follow the studies of [13, 20, 4] and consider an ensemble of sparse random graphs.From our numerical study, we have found that all of the heuristics tested share the following properties when the random graphs become large: i) each algorithm can be characterized by a fixed percentage excess above the optimum cost; ii) the ....

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J. W. Berry and M. K. Goldberg, Path optimization for graph partitioning problems, Discrete Appl. Math., 90 (1999), pp. 27--50.

....solution is given. The techniques used by these two approaches di#er greatly. Lang and Rao [14] conducted some experiments based on [13] and reported that the technique is successful for large graphs if long running times are allowed and if an additional clean up phase [8] is used. See also [1]. We unify the problems of b balanced cuts and k balanced partitions into a new problem called # separators. Given a parameter 0 # 1, the # separator problem is to find a minimum capacity cut that partitions the vertex set into connected components such that the weight of each is at most # ....

J. W. Beery and M. K. Goldberg, Path optimization for graph partitioning problems, Discrete Appl. Math., 90 (1999), pp. 27--50.

....such as logic partitioning [12] and placement [6, 19] Because of these applications, the GPP has been used as a testing ground for many heuristics. For our work, a selection had to be made; in view of the previous studies by Johnson et al. 13] Lang and Rao [20] and Berry and Goldberg [4], we have restricted our study to iterative improvement heuristics based on local search and to simulated annealing. Having made a choice of optimization problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the ....

....problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the structure of the actual instances of interest to the practitioner. Since we do not have a particular application in mind, we shall follow the studies of [13, 20, 4], and consider an ensemble of sparse random graphs. From our numerical study, we have found that all of the heuristics tested share the following properties when the random graphs become large: i) each algorithm can be characterized by a fixed percentage excess above the optimum cost; ii) the ....

[Article contains additional citation context not shown here]

J. W. Berry and M. K. Goldberg, Path optimization for graph partitioning problems. Special Issue on Combinatorial Algorithms for VLSI Design, submitted, 1998.

....such as logic partitioning [12] and placement [6, 17] Because of these applications, the GPP has been used as a testing ground for many heuristics. For our work, a selection had to be made; in view of the previous studies by Johnson et al. 13] Lang and Rao [18] and Berry and Goldberg [4], we have restricted our study to iterative improvement heuristics based on local search and to simulated annealing. Having made a choice of optimization problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the ....

....problem and algorithms, it remains to define the class of instances for the testbeds. Ideally, this family of instances should reflect the structure of the actual instances of interest to the practitioner. Since we do not have a particular application in mind, we shall follow the studies of [13, 18, 4], and consider an ensemble of sparse random graphs. From our numerical study, we have found that all of the heuristics tested share the following properties when the random graphs become large: i) each algorithm can be characterized by a fixed percentage excess above the optimum cost; ii) the ....

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J. W. Berry and M. K. Goldberg, Path optimization for graph partitioning problems. preprint, 1994.

.... [10, 23, 1] For instance, the approximation properties of sparse random graphs for different layout problems are considered in [18, 50] and partitioning algorithms for random graphs are studied in [11, 13] Event though many empirical studies have used random models of geometric graphs [30, 7, 19, 46, 34], its theoretical study has mainly focussed on parameters as their clique number or chromatic number, or in their connectivity properties [3, 4, 43, 44, 15] In this paper, we are concerned on the approximability of several layout problems on geometric random graphs. The layout problems that we ....

....for large graphs. It must be remarked, that while our algorithms use graphical information (the nodes coordinates and the radius) in order to build a layout, this information is not given as input in the problem definition. This simplification is an accepted common practice in the literature [30, 7, 34], even if the problem of recognizing geometric graphs is NP hard [12] 2 Definitions and related results Layout problems. We always consider as input undirected graphs without self loops. A layout on a graph G = V; E) is a one to one function : V [n] f1; ng with n = jV j. Given ....

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J. W. Berry and M. K. Goldberg. Path Optimization for Graph Partitioning Problems. Technical report TR: 95-34, DIMACS, 1995.

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J. Berry and M. Goldberg. Path optimization for graph partitioning problem. Discrete Applied Mathematics, 90:27--50, 1999.

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Berry, J., Goldberg, M., Path optimization for graph partitioning problems. Discrete Applied Mathematics 90 (1999) 27--50

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J. Berry and M. Goldberg, \Path Optimization for Graph Partitioning Problems,", Discrete Applied Mathematics (special issue on approximation algorithms), (90), pp. 27-50, 1999.

....that for any vertex v, G Gamma v is planar. The max cut problem remains NP hard for such cases. 2 Previous Work The history of work on approximate graph bisection problems dates back at least thirty years. We will not attempt to chronicle this work here. A more thorough review is presented in [Ber94]. An excellent survey of results in spectral and polyhedral approaches to the max cut problem is presented in [PT93] Below, we will give a very brief summary of the most familiar approaches to graph partitioning. The de facto benchmark algorithm for more than twenty five years has been the famous ....

....set of candidates. A similar vertex ordering technique was described in [CSS91] The W algorithm is so named since the construction of a partitioning represents a single walk down an implicit backtracking tree (where the other branches of the tree are due to possible non greedy placements. See [Ber94] for more details) 4.3 Algorithm Implementations Our implementations of the KL, SA, and PO algorithms all share the exact same bucket data structure code and were implemented in C as parts of a single system by the same programmer. Our version of KL was tested on the set of R G n;d graphs from ....

[Article contains additional citation context not shown here]

J. W. Berry. Path Optimization for Graph Partitioning Problems: A Case Study of Near Greedy Analysis. PhD thesis, Rensselaer Polytechnic Institute, Dec 1994.

....vertex v, G Gamma v is planar. The max cut problem remains NP hard for such cases. 3 2 Previous Work There history of work on approximate graph bisection problems dates back at least thirty years. We will not attempt to chronicle this work here. A more thorough review is presented in [Ber94]. An excellent survey of results in spectral and polyhedral approaches to the max cut problem is presented in [PT93] Below, we will give a very brief summary of the most familiar approaches to graph partitioning. The defacto benchmark algorithm for almost twenty five years has been the famous ....

....set of candidates. A similar vertex ordering technique was described in [CSS91] The W algorithm is so named since the construction of a partitioning represents a single walk down an implicit backtracking tree (where the other branches of the tree are due to possible non greedy placements. See [Ber94] for more details) 4.3 Algorithm Implementations Our implementations of the KL, SA, and PO algorithms all share the exact same bucket data structure code and were implemented in C as parts of a single system by the same programmer. Our version of KL was tested on the set of R G n;d graphs from ....

[Article contains additional citation context not shown here]

J. W. Berry. Path Optimization for Graph Partitioning Problems: A Case Study of Near Greedy Analysis. PhD thesis, Rensselaer Polytechnic Institute, Dec 1994.

No context found.

J. W. Berry and M. K. Goldberg. Path optimization for graph partitioning problems. Discrete Applied Mathematics. Combinatorial Algorithms, Optimization and Computer Science, 90(1-3):27--50, 1999.

No context found.

J. W. Berry and M. K. Goldberg, Path Optimization for Graph Partitioning Problems. Technical report TR: 95-34, DIMACS, 1995.

No context found.

J. W. Berry and M. K. Goldberg, Path Optimization for Graph Partitioning Problems. Technical report TR: 95-34, DIMACS, 1995.

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