The Experts below are selected from a list of 19845 Experts worldwide ranked by ideXlab platform
Hans-joachim Böckenhauer - One of the best experts on this subject based on the ideXlab platform.
-
steiner tree reoptimization in graphs with sharpened Triangle Inequality
Journal of Discrete Algorithms, 2012Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened @b-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+@c for an arbitrary small @c>0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time (1/2+@b)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (@b=1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2@b-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any @b<1/2+ln(3)/4~0.775.
-
the steiner tree reoptimization problem with sharpened Triangle Inequality
Technical report Swiss Federal Institute of Technology Zurich Department of Computer Science, 2010Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+ for an arbitrary small > 0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design lineartime (1/2+β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β = 1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β < 1/2 + ln(3)/4 0.775.
-
on k connectivity problems with sharpened Triangle Inequality
Journal of Discrete Algorithms, 2008Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Ralf Klasing, Sebastian Seibert, Dirk Bongartz, Guido Proietti, Walter UngerAbstract:The k-connectivity problem is to find a minimum-cost k-edge- or k-vertex-connected spanning subgraph of an edge-weighted, undirected graph G for any given G and k. Here, we consider its NP-hard subproblems with respect to the parameter @b, with 12<@b<1, where G=(V,E) is a complete graph with a cost function c satisfying the sharpened Triangle Inequality c({u,v})=<@[email protected]?(c({u,w})+c({w,v})) for all u,v,[email protected]?V. First, we give a simple linear-time approximation algorithm for these optimization problems with approximation ratio @[email protected] for any 12=<@b<1, which improves the known approximation ratios for 12<@b<23. The analysis of the algorithm above is based on a rough combinatorial argumentation. As the main result of this paper, for k=3, we sophisticate the combinatorial consideration in order to design a (1+5([email protected])9([email protected])+O(1|V|))-approximation algorithm for the 3-connectivity problem on graphs satisfying the sharpened Triangle Inequality for 12=<@b=<23. As part of the proof, we show that for each spanning 3-edge-connected subgraph H, there exists a spanning 3-regular 2-vertex-connected subgraph H^' of at most the same cost, and H can be transformed into H^' efficiently.
-
Approximation algorithms for the TSP with sharpened Triangle Inequality
Information Processing Letters, 2000Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Ralf Klasing, Sebastian Seibert, Walter UngerAbstract:Abstract The traveling salesman problem (TSP) is one of the hardest optimization problems in NPO because it does not admit any polynomial-time approximation algorithm (unless P = NP ). On the other hand we have a polynomial-time approximation scheme (PTAS) for the Euclidean TSP and the 3/2 -approximation algorithm of Christofides for TSP instances satisfying the Triangle Inequality. In this paper, we consider Δ β -TSP, for 1/2 , as a subproblem of the TSP whose input instances satisfy the β -sharpened Triangle Inequality cost({u,v})≤β(cost({u,x})+cost({x,v})) for all vertices u , v , x . This problem is APX-complete for every β>1/2 . The main contribution of this paper is the presentation of three different methods for the design of polynomial-time approximation algorithms for Δ β -TSP with 1/2 , where the approximation ratio lies between 1 and 3/2 , depending on β .
Juraj Hromkovič - One of the best experts on this subject based on the ideXlab platform.
-
steiner tree reoptimization in graphs with sharpened Triangle Inequality
Journal of Discrete Algorithms, 2012Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened @b-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+@c for an arbitrary small @c>0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time (1/2+@b)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (@b=1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2@b-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any @b<1/2+ln(3)/4~0.775.
-
the steiner tree reoptimization problem with sharpened Triangle Inequality
Technical report Swiss Federal Institute of Technology Zurich Department of Computer Science, 2010Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+ for an arbitrary small > 0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design lineartime (1/2+β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β = 1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β < 1/2 + ln(3)/4 0.775.
-
on k connectivity problems with sharpened Triangle Inequality
Journal of Discrete Algorithms, 2008Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Ralf Klasing, Sebastian Seibert, Dirk Bongartz, Guido Proietti, Walter UngerAbstract:The k-connectivity problem is to find a minimum-cost k-edge- or k-vertex-connected spanning subgraph of an edge-weighted, undirected graph G for any given G and k. Here, we consider its NP-hard subproblems with respect to the parameter @b, with 12<@b<1, where G=(V,E) is a complete graph with a cost function c satisfying the sharpened Triangle Inequality c({u,v})=<@[email protected]?(c({u,w})+c({w,v})) for all u,v,[email protected]?V. First, we give a simple linear-time approximation algorithm for these optimization problems with approximation ratio @[email protected] for any 12=<@b<1, which improves the known approximation ratios for 12<@b<23. The analysis of the algorithm above is based on a rough combinatorial argumentation. As the main result of this paper, for k=3, we sophisticate the combinatorial consideration in order to design a (1+5([email protected])9([email protected])+O(1|V|))-approximation algorithm for the 3-connectivity problem on graphs satisfying the sharpened Triangle Inequality for 12=<@b=<23. As part of the proof, we show that for each spanning 3-edge-connected subgraph H, there exists a spanning 3-regular 2-vertex-connected subgraph H^' of at most the same cost, and H can be transformed into H^' efficiently.
-
Approximation algorithms for the TSP with sharpened Triangle Inequality
Information Processing Letters, 2000Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Ralf Klasing, Sebastian Seibert, Walter UngerAbstract:Abstract The traveling salesman problem (TSP) is one of the hardest optimization problems in NPO because it does not admit any polynomial-time approximation algorithm (unless P = NP ). On the other hand we have a polynomial-time approximation scheme (PTAS) for the Euclidean TSP and the 3/2 -approximation algorithm of Christofides for TSP instances satisfying the Triangle Inequality. In this paper, we consider Δ β -TSP, for 1/2 , as a subproblem of the TSP whose input instances satisfy the β -sharpened Triangle Inequality cost({u,v})≤β(cost({u,x})+cost({x,v})) for all vertices u , v , x . This problem is APX-complete for every β>1/2 . The main contribution of this paper is the presentation of three different methods for the design of polynomial-time approximation algorithms for Δ β -TSP with 1/2 , where the approximation ratio lies between 1 and 3/2 , depending on β .
Bjorn Steffen - One of the best experts on this subject based on the ideXlab platform.
-
steiner tree reoptimization in graphs with sharpened Triangle Inequality
Journal of Discrete Algorithms, 2012Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened @b-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+@c for an arbitrary small @c>0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time (1/2+@b)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (@b=1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2@b-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any @b<1/2+ln(3)/4~0.775.
-
the steiner tree reoptimization problem with sharpened Triangle Inequality
Technical report Swiss Federal Institute of Technology Zurich Department of Computer Science, 2010Co-Authors: Hans-joachim Böckenhauer, Juraj Hromkovič, Karin Freiermuth, Tobias Momke, Andreas Sprock, Bjorn SteffenAbstract:In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-Triangle Inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened Triangle Inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+ for an arbitrary small > 0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design lineartime (1/2+β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β = 1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β < 1/2 + ln(3)/4 0.775.
Thomas S Huang - One of the best experts on this subject based on the ideXlab platform.
-
speeding up relevance feedback in image retrieval with Triangle Inequality based algorithms
International Conference on Acoustics Speech and Signal Processing, 2002Co-Authors: Ziyou Xiong, Xiang Zhou, William M Pottenger, Thomas S HuangAbstract:A content-based image retrieval(CBIR) system has been constructed to integrate relevance feedback with Triangle-Inequality based algorithms. The system offers typically 20 to 30 times faster retrieving speed with minimum sacrifice of retrieval performance on Corel database consisting of more than 17,000 images. The theoretic framework is built by using Triangle-Inequality based algorithms at sub-feature level and using relevance feedback techniques at feature level. Results show retrieval performance is clearly improved over the approach with only Triangle-Inequality based algorithms. A new high level weight updating method for the hierarchical distance model for relevance feedback is proposed.
-
ICASSP - Speeding up relevance feedback in image retrieval with Triangle-Inequality based algorithms
IEEE International Conference on Acoustics Speech and Signal Processing, 2002Co-Authors: Ziyou Xiong, Xiang Zhou, William M Pottenger, Thomas S HuangAbstract:A content-based image retrieval(CBIR) system has been constructed to integrate relevance feedback with Triangle-Inequality based algorithms. The system offers typically 20 to 30 times faster retrieving speed with minimum sacrifice of retrieval performance on Corel database consisting of more than 17,000 images. The theoretic framework is built by using Triangle-Inequality based algorithms at sub-feature level and using relevance feedback techniques at feature level. Results show retrieval performance is clearly improved over the approach with only Triangle-Inequality based algorithms. A new high level weight updating method for the hierarchical distance model for relevance feedback is proposed.
Sever S Dragomir - One of the best experts on this subject based on the ideXlab platform.
-
Reverses of the continuous Triangle Inequality for Bochner integral in complex Hilbert spaces
Journal of Mathematical Analysis and Applications, 2007Co-Authors: Sever S DragomirAbstract:Some reverses of the continuous Triangle Inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
-
Reverses of the Triangle Inequality via Selberg's and Boas-Bellman's Inequalities
2006Co-Authors: Sever S DragomirAbstract:Reverses of the Triangle Inequality for vectors in inner product spaces via the Selberg and Boas-Bellman generalisations of Bessel’s Inequality are given. Applications for complex numbers are also provided.
-
some reverses of the generalised Triangle Inequality in complex inner product spaces
Linear Algebra and its Applications, 2005Co-Authors: Sever S DragomirAbstract:Some reverses for the generalised Triangle Inequality in complex inner product spaces are given. They improve the classical Diaz-Metcalf inequalities. They are applied to obtain inequalities for complex numbers.
-
Reverses of the Triangle Inequality in Banach Spaces
arXiv: Classical Analysis and ODEs, 2005Co-Authors: Sever S DragomirAbstract:Recent reverses for the discrete generalised Triangle Inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for complex numbers and functions are pointed out as well.
-
Additive reverses of the generalized Triangle Inequality in normed spaces
arXiv: Metric Geometry, 2005Co-Authors: Sever S DragomirAbstract:Some additive reverses of the generalized Triangle Inequality in normed linear spaces are given. Applications for complex numbers are pro-vided as well.
