Given a set of terminals in the plane, a bottleneck Steiner tree is a tree interconnecting the terminals, in which the length of the longest edge is minimized. The bottleneck Steiner tree problem, or special cases the...
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Given a set of terminals in the plane, a bottleneck Steiner tree is a tree interconnecting the terminals, in which the length of the longest edge is minimized. The bottleneck Steiner tree problem, or special cases thereof, has applications in facility location and electronic physical design automation. In this paper, we first consider algorithms for computing optimal bottleneck Steiner trees. For a given topology, we give a direct, geometric algorithm that computes an optimal rectilinear bottleneck Steiner tree in O(n(2)) time, which improves on the time complexity of previous algorithms. We also give a linear-time algorithm that, given the output from the previous algorithm, computes a rectilinear Steiner tree with minimum bottleneck length and that, among all trees with minimum bottleneck length, has minimum total length. These topology-specific algorithms provide solutions to many facility location applications, and in combination with a topology enumeration algorithm, can be used to solve the more general problems that arise in other applications. We also describe some difficulties in generalizing these results to the Euclidean problem, and give a simple approximation algorithm for the Euclidean problem. We then consider computation of approximate bottleneck Steiner trees. Specifically, we derive the exact value of the bottleneck Steiner ratio in any distance metric. The bottleneck Steiner ratio is the maximum ratio of the length of the longest edge in a minimum spanning tree to the length of the longest edge in an optimal bottleneck Steiner tree. Thus, the bottleneck Steiner ratio indicates the quality of a minimum spanning tree as an approximation of an optimal bottleneck Steiner tree.
We describe a queueing theoretic approach to the delay analysis for the class of synchronous random-access protocols consisting of a Capetanakis-type tree Algorithm for conflict resolution and a window algorithm for c...
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This paper introduces two types of indirect covering tree problems using a spanning tree as a backbone network. The minimum cost covering subtree seeks the minimum cost collection of arcs that form a subtree and satis...
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This paper introduces two types of indirect covering tree problems using a spanning tree as a backbone network. The minimum cost covering subtree seeks the minimum cost collection of arcs that form a subtree and satisfy covering constraints for nodes of the network. Reduction techniques that have been used to solve the location set covering problem are extended to solve the Minimum Cost Covering Subtree (MCCS). The second problem, The Maximal Indirect Covering Subtree (MICS), chooses that subtree which maximizes the demand within a distance standard of nodes of the subtree. In addition, some variations of the maximal indirect covering subtree problem are proposed.
A greedy approach can be applied to find 2 edge-disjoint 1-trees or spanning trees (if they exist) of minimum total length in a graph with n vertices and m edges. A greedy algorithm to solve the tree problem contains ...
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A greedy approach can be applied to find 2 edge-disjoint 1-trees or spanning trees (if they exist) of minimum total length in a graph with n vertices and m edges. A greedy algorithm to solve the tree problem contains a routine that tests whether 2 edge-disjoint forests can be augmented with a given edge. Two test routines are discussed with different worst-case running times. The most efficient one is utilized to derive in O(m log m + n2) operations a lower bound solution to the 2-Peripatetic Salesman Problem (2-PSP), which requires 2 edge-disjoint Hamiltonian cycles of minimum total length. Then the other test routine executes in O(n2) operations a sensitivity analysis for all relevant edges. Computational results illustrate the impact of the sensitivity analysis.
Let K be contained in the vertex-set of a graph G. ''The most vital edge'' is the edge whose deletion yields the largest decrease in the K-terminal reliability, that is the probability that all vertice...
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Let K be contained in the vertex-set of a graph G. ''The most vital edge'' is the edge whose deletion yields the largest decrease in the K-terminal reliability, that is the probability that all vertices in K are connected. In this paper, we present a linear-time algorithm for finding the most vital edge with respect to K-terminal reliability in series-parallel networks.
The notion of orthonormal wavelet packets introduced by Coifman and Meyer is generalized to the nonorthogonal setting in order to include compactly supported and symmetric basis functions. In particular, dual (or bior...
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The notion of orthonormal wavelet packets introduced by Coifman and Meyer is generalized to the nonorthogonal setting in order to include compactly supported and symmetric basis functions. In particular, dual (or biorthogonal) wavelet packets are investigated and a stability result is established. algorithms for implementations are also developed.
The rectilinear Steiner ratio is the worst-case ratio of the length of a rectilinear minimum spanning tree to the length of a rectilinear Steiner minimal tree. Hwang proved that the ratio for point sets in the plane i...
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The rectilinear Steiner ratio is the worst-case ratio of the length of a rectilinear minimum spanning tree to the length of a rectilinear Steiner minimal tree. Hwang proved that the ratio for point sets in the plane is 3/2. We provide a simple proof of the 3/2-bound.
A dual ascent algorithm is described for the 1-tree relaxation of the symmetric traveling salesman problem. The ascent directions correspond to increasing (decreasing) the dual variables for the nodes of a set that is...
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A dual ascent algorithm is described for the 1-tree relaxation of the symmetric traveling salesman problem. The ascent directions correspond to increasing (decreasing) the dual variables for the nodes of a set that is out of kilter high (low) for all 1-trees that are optimal at the current dual solution. This algorithm is shown to obtain near optimal bounds in about one-quarter of the time required by the subgradient method on a sample of well-known test cases.
A new reconfigurable systolic multicomputer architecture is presented. The proposed architecture, called the C ylindrical B anyan M ulticomputer (CBM), is based on the structure of a modified banyan network where ever...
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A new reconfigurable systolic multicomputer architecture is presented. The proposed architecture, called the C ylindrical B anyan M ulticomputer (CBM), is based on the structure of a modified banyan network where every node of the network graph is composed of an application processor, a local memory and a communication processor, and network's inputs and outputs are merged (fused). The CBM has one of the lowest (cost) X (delay) among known multicomputer architectures based on regular networks. It is shown that a variety of computation structures such as pipelines, rings, and trees may be constructed and reconfigured in an optimal or a nearby optimal way on the CBM architecture, and that various basic algorithms can be executed very efficiently in a systolic manner. It is also shown that the CBM is an easily diagnosable and fault-tolerant system.
The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P 1 and P 2 . If P is a mixture of two (approxim...
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The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P 1 and P 2 . If P is a mixture of two (approximately) Gaussian subpopulations, then P 1 and P 2 are good approximations to the original Gaussians, if their Fisher distance is great enough. Moreover, good approximations to P 1 and P 2 can be obtained by dividing P into small parts; finding the maximum-distance (MD) subdivision of each part; combining small groups of these subdivisions into (approximate) MD subdivisions of larger parts; and so on. This divide-and-conquer approach yields an approximate MD subdivision of P in O (log n ) computational steps using O ( n ) processors, where n is the size of P .
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