Article
A polylogarithmic approximation for computing nonmetric terminal Steiner trees.
Information Processing Letters
(Impact Factor: 0.48).
09/2010;
110:826829.
DOI: 10.1016/j.ipl.2010.07.006
Source: DBLP
 References (14)

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Chapter: Approximation Algorithms
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ABSTRACT: Most interesting realworld optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a nearoptimal solution to a largescale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization problems by considering how the computational demands of a solution method grow with the size of the problem instance to be solved (see e.g. Chapter 11 or Aho et al., 1979). A key distinction is made between problems that require computational resources that grow polynomially with problem size versus those for which the required resources grow exponentially. The former category of problems are called efficiently solvable, whereas problems in the latter category are deemed intractable because the exponential growth in required computational resources renders all but the smallest instances of such problems unsolvable.03/2006: pages 557585; 
Conference Paper: Polylogarithmic inapproximability.
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ABSTRACT: We provide the first hardness result of a polylogarithmic approximation ratio for a natural NPhard optimization problem. We show that for every fixed ε>0, the GROUPSTEINERTREE problem admits no efficient log2ε k approximation, where k denotes the number of groups (or, alternatively, the input size), unless NP has quasi polynomial LasVegas algorithms. This hardness result holds even for input graphs which are Hierarchically WellSeparated Trees, introduced by Bartal [FOCS, 1996]. For these trees (and also for general trees), our bound is nearly tight with the logsquared approximation currently known. Our results imply that for every fixed ε>0, the DIRECTEDSTEINER TREE problem admits no log2ε napproximation, where n is the number of vertices in the graph, under the same complexity assumption.Proceedings of the 35th Annual ACM Symposium on Theory of Computing, June 911, 2003, San Diego, CA, USA; 01/2003 
Article: The full Steiner tree problem
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ABSTRACT: Motivated by the reconstruction of phylogenetic tree in biology, we study the full Steiner tree problem in this paper. Given a complete graph G=(V,E) with a length function on E and a proper subset R⊂V, the problem is to find a full Steiner tree of minimum length in G, which is a kind of Steiner tree with all the vertices of R as its leaves. In this paper, we show that this problem is NPcomplete and MAX SNPhard, even when the lengths of the edges are restricted to either 1 or 2. For the instances with lengths either 1 or 2, we give a approximation algorithm to find an approximate solution for the problem.Theoretical Computer Science 09/2003; 306(13306):5567. DOI:10.1016/S03043975(03)002093 · 0.52 Impact Factor
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