Unit disk graph recognition is NP-hard

Breu, Heinz; Kirkpatrick, David G.

doi:10.1016/s0925-7721(97)00014-x

Cited by 251 publications

(189 citation statements)

References 7 publications

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“…It is observed, as theoretically expected, that as the radius of emission increases the angle of emission necessary to ensure the same probability of success decreases. As colisions are taken into account one observe on Figures 4,5,6 that increasing the angle of emissions increases initially the chance of success up to a maximal value and afterwards the chance of succes decreases. On these figures one can also observe that for large value of the emission angle, the performances are better with small radius of emission.…”

Section: Methodsmentioning

confidence: 96%

“…In [13,14] the authors consider a particular technique for estimating the distances between sensors and proceed to real experiments based on Motes 1 sensor systems. From a complexity point of view, in [3,6] NP-hardness results are provided for the localization and connex problems. These results support the application of approximation algorithms and numerical investigations.…”

Section: Related Workmentioning

confidence: 99%

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Numerical Estimation of the Impact of Interferences on the Localization Problem in Sensor Networks

Bouget

Leone

Rolim

2006

Experimental Algorithms

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Abstract.In this paper we numerically analyze the impact of interferences in wireless networks. More particularly, the impact on the probability of success of a localization algorithm. This problem is particularly relevant in the context of sensor networks. Actually, our numerical experiments provide information about this algorithm, even when we do not consider interferences. Indeed, in this case, sharp threshold is observed on the probability of success of the algorithm. Moreover, our numerical computations show that the main harmful interferences are the ones occurring between sensors which get localized at the same time and send in turn their own location. This is demonstrated by varying the time span of the random waiting time before the emissions. We then observe that the longer the waiting time the closer the curves are to the ones obtained without considering interferences. Hence, this proves to be an efficient way of reducing the impact of interferences on the localization algorithm. Moreover, our numerical experiments demonstrate that among the sectors of disk with same area, the one with the smaller radius of emission and larger angle of emission is the more appropriate to the localization algorithm.

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Section: Methodsmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

Numerical Estimation of the Impact of Interferences on the Localization Problem in Sensor Networks

Bouget

Leone

Rolim

2006

Experimental Algorithms

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“…In this large scale effort, we address the second step of the protein folding prediction problem: the reconstruction of the 3D protein structure from its contact map. The general version of this problem has been proved to be NP-hard (Breu et al, 1998). Various heuristic algorithms have been proposed to solve the problem (Galaktionov, 1994;Vendruscolo, 1997;Bohr, 1993;Pollastri, 2006) but most of these methods have been tested only on the relative predictions and none of them are available to the scientific community.…”

Section: Case Study 3: "Ft-comar: a Large Scale Application For Reconmentioning

confidence: 99%

The LIBI Grid Platform for Bioinformatics

2009

Handbook of Research on Computational Grid Technologies for Life Sciences, Biomedicine, and Healthcare

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The LIBI project (International Laboratory of BioInformatics), which started in 2005 and will end in 2009, was initiated with the aim of setting up an advanced bioinformatics and computational biology laboratory, focusing on basic and applied research in modern biology and biotechnologies. One of the 2 goals of this project has been the development of a Grid Problem Solving Environment, built on top of EGEE, DEISA and SPACI infrastructures, to allow the submission and monitoring of jobs mapped to complex experiments in bioinformatics. In this work we describe the architecture of this environment and describe several case studies and related results which have been obtained using it.

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“…If d ij is above the given threshold ðCM½i; j ¼ 0Þ but close to the threshold, then PERTURBATE changes the coordinates of i and j in order to make them a bit more distant (lines [6][7][8]. A perturbation can introduce new errors to the coordinate set, but conversely, it avoids not well-placed residues from getting stuck.…”

Section: Second Phase: Refinement Of the Coordinatesmentioning

confidence: 99%

Reconstruction of 3D Structures from Protein Contact Maps

Vassura

Margara

Medri

et al. 2007

Bioinformatics Research and Applications

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Abstract-The prediction of the protein tertiary structure from solely its residue sequence (the so-called Protein Folding Problem) is one of the most challenging problems in Structural Bioinformatics. We focus on the protein residue contact map. When this map is assigned, it is possible to reconstruct the 3D structure of the protein backbone. The general problem of recovering a set of 3D coordinates consistent with some given contact map is known as a unit-disk-graph realization problem, and it has been recently proven to be NP-hard. In this paper, we describe a heuristic method (COMAR) that is able to reconstruct with an unprecedented rate (3-15 seconds) a 3D model that exactly matches the target contact map of a protein. Working with a nonredundant set of 1,760 proteins, we find that the scoring efficiency of finding a 3D model very close to the protein native structure depends on the threshold value adopted to compute the protein residue contact map. Contact maps whose threshold values range from 10 to 18 Angstroms allow reconstructing 3D models that are very similar to the proteins' native structure.

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Unit disk graph recognition is NP-hard

Cited by 251 publications

References 7 publications

Numerical Estimation of the Impact of Interferences on the Localization Problem in Sensor Networks

Numerical Estimation of the Impact of Interferences on the Localization Problem in Sensor Networks

The LIBI Grid Platform for Bioinformatics

Reconstruction of 3D Structures from Protein Contact Maps

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