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15
Fixedparameter algorithms for protein similarity search under mRNA structure constraints
 In Proc. of the 31st international Workshop on Graphtheoretic concepts in computer science (WG
, 2005
"... Abstract. In the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codonwise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the socalled mRNA Structure Optimization ( ..."
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Cited by 9 (1 self)
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Abstract. In the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codonwise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the socalled mRNA Structure Optimization (MRSO) problem. Since MRSO is known to be APXhard, Bongartz [10] suggested to attack the problem using the approach of parameterized complexity. In this paper we propose three fixedparameter algorithms that apply for several interesting parameters of MRSO. We believe these algorithms to be relevant for practical applications today, as well as for possible future applications. Furthermore, our results extend the known tractability borderline of MRSO, and provide new research horizons for further improvements of this sort.
Fixed linear crossing minimization by reduction to the maximum cut problem
 in Proc 12th Ann. Int. Computing and Combinatorics Conference (COCOON’06
"... Abstract. Many reallife scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a way that the number of edge crossings is minimized. In this paper, we study a restricted version of the linear ..."
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Cited by 6 (0 self)
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Abstract. Many reallife scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a way that the number of edge crossings is minimized. In this paper, we study a restricted version of the linear layout problem where the order of vertices on the line is fixed, the socalled fixed linear crossing number problem (FLCNP). We show that this N Phard problem can be reduced to the wellknown maximum cut problem. The latter problem was intensively studied in the literature; efficient exact algorithms based on the branchandcut technique have been developed. By an experimental evaluation on a variety of graphs, we show that using this reduction for solving FLCNP compares favorably to earlier branchandbound algorithms. 1
Crossing Minimization for Symmetries
 Proc. of ISAAC 2002, Lecture Notes in Computer Science
, 2002
"... We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NPhard, even if the order of orbits around the rotation center or along the reection axis is fixed. Nevertheless, there is a linear time algorithm to test ..."
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Cited by 5 (4 self)
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We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NPhard, even if the order of orbits around the rotation center or along the reection axis is fixed. Nevertheless, there is a linear time algorithm to test planarity and to construct a planar embedding if possible. Finally, we devise an O(m log m) algorithm for computing a crossing minimal drawing if interorbit edges may not cross orbits, showing in particular that intraorbit edges do not contribute to the NPhardness of the crossing minimization problem for symmetries.
Line crossing minimization on metro maps
, 2007
"... We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V,E), so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying ..."
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Cited by 2 (1 self)
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We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V,E), so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway line which connects them, whereas the paths illustrate the lines connecting terminal stations. We call this the metroline crossing minimization problem (MLCM). In contrast to the problem of drawing the underlying graph nicely, MLCM has received fewer attention. It was recently introduced by Benkert et. al in [2]. In this paper, as a first step towards solving MLCM in arbitrary graphs, we study path and tree networks. We examine several variations of the problem for which we develop algorithms for obtaining optimal solutions.
An improved neural network model for the 2page crossing number problem
 IEEE Trans. on Neural Networks
"... This item was submitted to Loughborough’s Institutional Repository by the ..."
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Cited by 2 (0 self)
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This item was submitted to Loughborough’s Institutional Repository by the
On MetroLine Crossing Minimization
, 2010
"... We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V, E) so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying n ..."
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Cited by 1 (0 self)
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We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V, E) so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway track connecting them, whereas the paths illustrate the metro lines connecting terminal stations. We call this the metroline crossing minimization problem (MLCM). We examine several variations of the problem for which we develop algorithms that yield optimal solutions.
Multilevel verticality optimization: Concept, strategies, and drawing scheme
, 2011
"... Abstract. In traditional multilevel graph drawing—known as Sugiyama’s framework—the number of crossings is considered one of the most important goals. Herein, we propose the alternative concept of optimizing the verticality of the drawn edges. We formally specify the problem, discuss its relative m ..."
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Abstract. In traditional multilevel graph drawing—known as Sugiyama’s framework—the number of crossings is considered one of the most important goals. Herein, we propose the alternative concept of optimizing the verticality of the drawn edges. We formally specify the problem, discuss its relative merits, and show that drawings that are good w.r.t. verticality in fact also have a low number of crossings. We present heuristic and exact approaches to tackle the verticality problem and study them in practice. Furthermore, we present a new drawing scheme (inherently bundling edges and drawing them monotonously), especially suitable for verticality optimization. It works without the traditional subdivision of edges, i.e., edges may span multiple levels, and therefore potentially allows to tackle larger graphs. 1
DOI: 10.7155/jgaa.00267 How to Visualize the Kroot Name Server
, 2012
"... We present a novel paradigm to visualize the evolution of the service provided by one of the most popular root name servers, called Kroot, operated by the RIPE Network Coordination Centre (RIPE NCC) and distributed in several locations (instances) worldwide. Our approach can be usedtoeither monitor ..."
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We present a novel paradigm to visualize the evolution of the service provided by one of the most popular root name servers, called Kroot, operated by the RIPE Network Coordination Centre (RIPE NCC) and distributed in several locations (instances) worldwide. Our approach can be usedtoeither monitor what happenedduringaprescribed time interval or observe the status of the service in near realtime. We visualize how and when the clients of Kroot migrate from one instance to another, how the workload associated with each instance changes over time, and what are the instances that contribute to offer the service to a selected Internet Service Provider. In addition, the visualization aims at distinguishing usual from unusual operational patterns. This helps not only to improve the quality of the service but also to spot securityrelated issues and to investigate unexpected routing changes. Submitted: