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Simulated annealing for graph bisection
 in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science
, 1993
"... We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in Gnpr when p r = O(n*’) for A 5 2. (The random graph model Gnpr specifies a “planted ” bisection of density r, ..."
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Cited by 35 (1 self)
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We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in Gnpr when p r = O(n*’) for A 5 2. (The random graph model Gnpr specifies a “planted ” bisection of density r, separating two n/2vertex subsets of slightly higher density p.) We show that simulated “annealing ” at an appropriate fixed temperature (i.e., the Metropolis algorithm) finds the unique smallest bisection in O(n2+‘) steps with very high probability, provided A> 1116. (By using a slightly modified neighborhood structure, the number of steps can be reduced to O(n’+‘).) We leave open the question of whether annealing is effective for A in the range 312 < A 5 1116, whose lower limit represents the threshold at which the planted bisection becomes lost amongst other random small bisections. It also remains open whether hillclimbing (i.e., annealing at temperature 0) solves the same problem. 1
Path Optimization for Graph Partitioning Problems
 Discrete Applied Mathematics. Combinatorial Algorithms, Optimization and Computer Science
, 1998
"... This paper presents a new heuristic for graph partitioning called Path Optimization (PO), and the results of an extensive set of empirical comparisons of the new algorithm with two very wellknown algorithms for partitioning: the KernighanLin algorithm and simulated annealing. Our experiments are ..."
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Cited by 13 (2 self)
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This paper presents a new heuristic for graph partitioning called Path Optimization (PO), and the results of an extensive set of empirical comparisons of the new algorithm with two very wellknown algorithms for partitioning: the KernighanLin algorithm and simulated annealing. Our experiments are described in detail, and the results are presented in such a way as to reveal performance trends based on several variables. Sufficient trials are run to obtain 99% confidence intervals small enough to lead to a statistical ranking of the implementations for various circumstances. The results for geometric graphs, which have become a frequentlyused benchmark in the evaluation of partitioning algorithms, show that PO holds an advantage over the others. In addition to the main test suite described above, comparisons of PO to more recent partitioning approaches are also given. We present the results of comparisons of PO with a parallelized implementation of Goemans' and Williamson's 0.878 appr...
Path Optimization and NearGreedy Analysis for Graph Partitioning: An Empirical Study
 Study, Proceedings of the 1995 Symposium on Discrete Algorithms
, 1995
"... This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max cut problem and the min quotient cut problem. We present the results of computational compari ..."
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Cited by 9 (7 self)
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This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max cut problem and the min quotient cut problem. We present the results of computational comparisons between this technique and the KernighanLin algorithm, the simulated annealing algorithm, the FLOWalgorithm of [17], the multilevel spectral algorithm of [14], and the recent 0.878approximation algorithm of [7]. The experiments were conducted on two classes of graphs that have become standard for such tests: random and random geometric. They show that for both classes of inputs and both variations of the problem, the new heuristic is competitive with the other algorithms, and holds a advantage for min quotient cut when applied to very large, sparse geometric graphs (10,000  100,000 vertices, average degree 10). In the last part of the paper, we describe an approach to analyzing gr...
Their Problems Are My Problems  The Transition between Internal and External Conflict
 CONFLICTING AGENTS: CONFLICT MANAGEMENT IN MULTIAGENT SYSTEMS, MULTIAGENT SYSTEMS, ARTIFICIAL SOCIETIES, AND SIMULATED ORGANIZATIONS, CHAPTER 3
, 2000
"... In MultiAgent Systems there has been quite an amount of research on how to model conflicts in (intelligent) agent architectures for example by imitating mental states and augmenting them with social notions. Nevertheless, a great deal of investigation is missing on the transition between internal a ..."
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Cited by 3 (0 self)
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In MultiAgent Systems there has been quite an amount of research on how to model conflicts in (intelligent) agent architectures for example by imitating mental states and augmenting them with social notions. Nevertheless, a great deal of investigation is missing on the transition between internal and external conflicts. Arguments in favor of taking a closer look at this transition include a practical one from applications where internal conflicts may easily become external conflicts and vice versa, and a technical one motivated by the existence of more efficient algorithms for solving internal conflicts. In tjis
A Formalization of Autonomous Dynamic Reconfiguration in Distributed Constraint Satisfaction
, 2000
"... Several interesting practical problems in process control, planning and scheduling can be expressed and solved using the model of constraint satisfaction problems. At least four drawbacks of this classical model directly relate to areas of distribution: complexity, scalability, privacy and robust ..."
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Cited by 2 (1 self)
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Several interesting practical problems in process control, planning and scheduling can be expressed and solved using the model of constraint satisfaction problems. At least four drawbacks of this classical model directly relate to areas of distribution: complexity, scalability, privacy and robustness. Hence, research on distributed constraint satisfaction problems is a new direction in the area of multiagent systems. A typical engineering task in distributed constraint satisfaction is the design of the distribution itself. A careful look at this task reveals that the design of distribution is critical to the quality and efficiency of the problem solving process and is itself an optimization problem.
High Performance Interconnection Networks
, 2002
"... The thesis is concerned with the design of high performance interconnection networks for use predominantly in parallel computing systems and wide area networks. The most important indicating a combined measure of hardware complexity and worstcast message routing complexity. Furthermore, a high perf ..."
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The thesis is concerned with the design of high performance interconnection networks for use predominantly in parallel computing systems and wide area networks. The most important indicating a combined measure of hardware complexity and worstcast message routing complexity. Furthermore, a high performance network should also have the properties of regular and planar topology, high bisection width and routing simplicity. Specifically, the following problems are studied: (i) constructing the largest possible networks that simultaneously exhibit a number of other properties including a small number of edges, high bisection width and planarity; and (ii) implementing high performance communication networks on a scale comparable to that of the Internet. With respect to specific technology, the thesis addresses the following two questions: (i) exactly how can optical internetworking be achieved on a world wide scale so as to maximize performance and (ii) just how big can an optical internetwork be, given the present/future technological limits and performance constraints. Major
Spectral Methods for Bisecting Graphs
, 1993
"... this paper have found widespread use in this application [24, 30]. Given the utility of graph bisection, it is disappointing (though not surprising) that this problem is difficult from a complexity pointofview. For general graphs, Garey, Johnson, and Stockmeyer [21] (see also [10]) have shown that ..."
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this paper have found widespread use in this application [24, 30]. Given the utility of graph bisection, it is disappointing (though not surprising) that this problem is difficult from a complexity pointofview. For general graphs, Garey, Johnson, and Stockmeyer [21] (see also [10]) have shown that the decision problem, "Does graph G have a bisection with fewer than k edges?" is NPcomplete. For planar graphs the complexity is unknown, but Papadimitriou and Sideri [28] conjecture that the problem is still NPcomplete. Polynomial time algorithms for finding optimal bisections are known only for trees, boundedwidth planar graphs, and solid grid graphs [28]. Furthermore, no approximation algorithms are known even for planar graphs. The current stateoftheart consists of heuristics that often perform well in practice [2, 4, 11, 25] and algorithms that have been shown to have good average case behavior over certain probability distributions on graphs [7, 9, 11, 14]. The next section briefly surveys some of these algorithms. The rest of this paper focuses on the spectral methods and is organized as follows. Section 3 covers some preliminary facts concerning the eigenvalues and eigenvectors of real, symmetric matrices. This section concludes with two theorems that play a central role in the two spectral algorithms that we will study. One of these two theorems is a slight generalization of a theorem due to Fan [15] that forms the basis for Section 4's simplified exposition of an algorithm due to Barnes [2]. The other theorem fills in a major hole in Boppana's extended abstract [7]. Boppana's algorithm is the topic of Section 5. We point out a problem with the original algorithm, discuss a remedy proposed by Boppana [8], and then demonstrate the problem with the remedy. Fo...