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An Improved Approximation Algorithm for the Asymmetric TSP with Strengthened Triangle Inequality
 Journal of Discrete Algorithms
, 2004
"... We consider the asymmetric traveling salesperson problem with #parameterized triangle inequality for # 2 , 1). That means, the edge weights fulfill w(u, v) (w(u, x) + w(x, v)) for all nodes u, v, x. Chandran and Ram [8] recently gave the first constant factor approximation algorithm with poly ..."
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Cited by 31 (8 self)
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We consider the asymmetric traveling salesperson problem with #parameterized triangle inequality for # 2 , 1). That means, the edge weights fulfill w(u, v) (w(u, x) + w(x, v)) for all nodes u, v, x. Chandran and Ram [8] recently gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio . We devise an approximation algorithm with performance 3 , which is better than the one of Chandran and Ram for # [0.5437, 1), that is, for the particularly interesting large values of #.
On the hardness of reoptimization
 In Proc. of the 34th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2008), volume 4910 of LNCS
, 2008
"... Abstract. We consider the following reoptimization scenario: Given an instance of an optimization problem together with an optimal solution, we want to find a highquality solution for a locally modified instance. The naturally arising question is whether the knowledge of an optimal solution to the ..."
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Cited by 14 (3 self)
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Abstract. We consider the following reoptimization scenario: Given an instance of an optimization problem together with an optimal solution, we want to find a highquality solution for a locally modified instance. The naturally arising question is whether the knowledge of an optimal solution to the unaltered instance can help in solving the locally modified instance. In this paper, we survey some partial answers to this questions: Using some variants of the traveling salesman problem and the Steiner tree problem as examples, we show that the answer to this question depends on the considered problem and the type of local modification and can be totally different: For instance, for some reoptimization variant of the metric TSP, we get a 1.4approximation improving on the best known approximation ratio of 1.5 for the classical metric TSP. For the Steiner tree problem on graphs with bounded cost function, which is APXhard in its classical formulation, we even obtain a PTAS for the reoptimization variant. On the other hand, for a variant of TSP, where some vertices have to be visited before a prescribed deadline, we are able to show that the reoptimization problem is exactly as hard to approximate as the original problem.
The Computational Complexity of Orientation Search in CryoElectron Microscopy
 Computational Science – ICCS 2004. Volume 3036 of Lecture Notes in Computer Science
, 2004
"... In this paper we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images an ..."
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Cited by 1 (1 self)
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In this paper we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and it has been studied intensively for more than 30 years.
The Computational Complexity of Orientation Search Problems in CryoElectron Microscopy
, 2004
"... In this report we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and ..."
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Cited by 1 (1 self)
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In this report we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and it has been studied intensively for more than 30 years.
Finland The Computational Complexity of Orientation Search Problems in CryoElectron Microscopy
, 2004
"... In this paper we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and i ..."
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In this paper we study the problem of determining threedimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and it has been studied intensively for more than 30 years. We analyze the computational complexity of the orientation problem and show that while several variants of the problem are NPhard, inapproximable and fixedparameter intractable, some restrictions are polynomialtime approximable within a constant factor or even solvable in logarithmic space. The orientation search problem is formalized as a constrained line arrangement problem that is of independent interest. The negative complexity results give a partial justification for the heuristic methods used in orientation search, and the positive complexity results on the orientation search have some positive implications also to the problem of finding functionally analogous genes.
THE TRAVELING SALESMAN PROBLEM UNDER SQUARED EUCLIDEAN DISTANCES
, 2010
"... Abstract. Let P be a set of points in R d, and let α � 1 be a real number. We define the distance between two points p,q ∈ P as pq  α, where pq  denotes the standard Euclidean distance between p and q. We denote the traveling salesman problem under this distance function by Tsp(d,α). We design a ..."
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Abstract. Let P be a set of points in R d, and let α � 1 be a real number. We define the distance between two points p,q ∈ P as pq  α, where pq  denotes the standard Euclidean distance between p and q. We denote the traveling salesman problem under this distance function by Tsp(d,α). We design a 5approximation algorithm for Tsp(2,2) and generalize this result to obtain an approximation factor of 3 α−1 + √ 6 α /3 for d = 2 and all α � 2. We also study the variant RevTsp of the problem where the traveling salesman is allowed to revisit points. We present a polynomialtime approximation scheme for RevTsp(2, α) with α � 2, and we show that RevTsp(d,α) is apxhard if d � 3 and α> 1. The apxhardness proof carries over to Tsp(d, α) for the same parameter ranges. 1.
www.stacsconf.org THE TRAVELING SALESMAN PROBLEM UNDER SQUARED EUCLIDEAN DISTANCES
"... Abstract. Let P be a set of points in R d, and let α � 1 be a real number. We define the distance between two points p,q ∈ P as pq  α, where pq  denotes the standard Euclidean distance between p and q. We denote the traveling salesman problem under this distance function by Tsp(d,α). We design a ..."
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Abstract. Let P be a set of points in R d, and let α � 1 be a real number. We define the distance between two points p,q ∈ P as pq  α, where pq  denotes the standard Euclidean distance between p and q. We denote the traveling salesman problem under this distance function by Tsp(d,α). We design a 5approximation algorithm for Tsp(2,2) and generalize this result to obtain an approximation factor of 3 α−1 + √ 6 α /3 for d = 2 and all α � 2. We also study the variant RevTsp of the problem where the traveling salesman is allowed to revisit points. We present a polynomialtime approximation scheme for RevTsp(2, α) with α � 2, and we show that RevTsp(d,α) is apxhard if d � 3 and α> 1. The apxhardness proof carries over to Tsp(d, α) for the same parameter ranges. 1.
Multi Perspective Metrics for Finding All Efficient Solutions to BiCriteria Travelling Salesman Problem
"... AbstractThe investigation of metrics in multiple perspectives is dealt in this paper for a bicriteria travelling salesman problem (BTSP). By representing the problem in a graphical view, its corresponding metrics in terms of graph theory is estimated. With the programming viewpoint a program using ..."
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AbstractThe investigation of metrics in multiple perspectives is dealt in this paper for a bicriteria travelling salesman problem (BTSP). By representing the problem in a graphical view, its corresponding metrics in terms of graph theory is estimated. With the programming viewpoint a program using Java programming language is implemented to solve a BTSP. The development of efficient software requires metrics, which is measured to highlight the performance of the software. The application can also be viewed in management perspective through which the solutions in reality are discussed. These approaches can be served as an essential device for the decision makers when they are dealing different varieties of logistics problems comprising two criterions.