
MultiLevel Steiner Trees
In the classical Steiner tree problem, one is given an undirected, conne...
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Approximation algorithms for priority Steiner tree problems
In the Priority Steiner Tree (PST) problem, we are given an undirected g...
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Computing VertexWeighted MultiLevel Steiner Trees
In the classical vertexweighted Steiner tree problem (VST), one is give...
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A General Framework for Multilevel Subsetwise Graph Sparsifiers
Given an undirected weighted graph $G(V,E)$, a subsetwise sparsifier ove...
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Multilevel Weighted Additive Spanners
Given a graph G = (V,E), a subgraph H is an additive +β spanner if _H(u,...
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Multilevel tree based approach for interactive graph visualization with semantic zoom
A recent data visualization literacy study shows that most people cannot...
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Approximation algorithms and an integer program for multilevel graph spanners
Given a weighted graph G(V,E) and t > 1, a subgraph H is a tspanner of...
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Kruskalbased approximation algorithm for the multilevel Steiner tree problem
We study the multilevel Steiner tree problem: a generalization of the Steiner tree problem in graphs, in which the terminals T require different levels, or equivalently, have different priorities. The problem requires that terminals be connected with edges satisfying their priority requirements and has applications in network design and multilevel graph visualization. The case where edge costs are proportional to their priority is approximable to within a constant factor from the optimal solution. For the more general case of nonproportional costs, the problem is hard to approximate to within a ratio of loglog n, where n is the number of vertices in the graph. A simple greedy algorithm by Charikar et al., however, provides a min{2(ln T+1), ℓρ}approximation in this setting. In this paper, we describe a natural generalization to the multilevel case of the classical (singlelevel) Steiner tree approximation algorithm based on Kruskal's minimum spanning tree algorithm. We prove that this algorithm achieves an approximation ratio at least as good as Charikar et al., and experimentally performs better with respect to the optimum solution. We develop an integer linear programming formulation to compute an exact solution for the multilevel Steiner tree problem with nonproportional edge costs and use it to evaluate the performance of our algorithm.
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