004 Datenverarbeitung; Informatik
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In this paper we study connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) by adding edges such that the resulting graph keeps the property. The aim is to add as few edges as possible. The property that we consider is planarity, both in an abstract graph-theoretic and in a geometric setting, where vertices correspond to points in the plane and edges to straight-line segments.
We show that it is NP-hard to nd a minimum-cardinality augmentation that makes a planar graph 2-edge connected. For making a planar graph 2-vertex connected this was known. We further show that both problems are hard in the geometric setting, even when restricted to trees. The problems remain hard for higher degrees of connectivity. On the other hand we give polynomial-time algorithms for the special case of convex geometric graphs.
We also study the following related problem. Given a planar (plane geometric) graph G, two vertices s and t of G, and an integer c, how many edges have to be added to G such that G is still planar (plane geometric) and contains c edge- (or vertex-) disjoint s{t paths? For the planar case we give a linear-time algorithm for c = 2. For the plane geometric case we give optimal worst-case bounds for c = 2; for c = 3 we characterize the cases that have a solution.
Background:
Chloroplast-encoded genes (matK and rbcL) have been formally proposed for use in DNA barcoding efforts targeting embryophytes. Extending such a protocol to chlorophytan green algae, though, is fraught with problems including non homology (matK) and heterogeneity that prevents the creation of a universal PCR toolkit (rbcL). Some have advocated the use of the nuclear-encoded, internal transcribed spacer two (ITS2) as an alternative to the traditional chloroplast markers. However, the ITS2 is broadly perceived to be insufficiently conserved or to be confounded by introgression or biparental inheritance patterns, precluding its broad use in phylogenetic reconstruction or as a DNA barcode. A growing body of evidence has shown that simultaneous analysis of nucleotide data with secondary structure information can overcome at least some of the limitations of ITS2. The goal of this investigation was to assess the feasibility of an automated, sequence-structure approach for analysis of IT2 data from a large sampling of phylum Chlorophyta.
Methodology/Principal Findings:
Sequences and secondary structures from 591 chlorophycean, 741 trebouxiophycean and 938 ulvophycean algae, all obtained from the ITS2 Database, were aligned using a sequence structure-specific scoring matrix. Phylogenetic relationships were reconstructed by Profile Neighbor-Joining coupled with a sequence structure-specific, general time reversible substitution model. Results from analyses of the ITS2 data were robust at multiple nodes and showed considerable congruence with results from published phylogenetic analyses.
Conclusions/Significance:
Our observations on the power of automated, sequence-structure analyses of ITS2 to reconstruct phylum-level phylogenies of the green algae validate this approach to assessing diversity for large sets of chlorophytan taxa. Moreover, our results indicate that objections to the use of ITS2 for DNA barcoding should be weighed against the utility of an automated, data analysis approach with demonstrated power to reconstruct evolutionary patterns for highly divergent lineages.
Practical optimization problems often comprise several incomparable and conflicting objectives. When booking a trip using several means of transport, for instance, it should be fast and at the same time not too expensive. The first part of this thesis is concerned with the algorithmic solvability of such multiobjective optimization problems. Several solution notions are discussed and compared with respect to their difficulty. Interestingly, these solution notions are always equally difficulty for a single-objective problem and they differ considerably already for two objectives (unless P = NP). In this context, the difference between search and decision problems is also investigated in general. Furthermore, new and improved approximation algorithms for several variants of the traveling salesperson problem are presented. Using tools from discrepancy theory, a general technique is developed that helps to avoid an obstacle that is often hindering in multiobjective approximation: The problem of combining two solutions such that the new solution is balanced in all objectives and also mostly retains the structure of the original solutions. The second part of this thesis is dedicated to several aspects of systems of equations for (formal) languages. Firstly, conjunctive and Boolean grammars are studied, which are extensions of context-free grammars by explicit intersection and complementation operations, respectively. Among other results, it is shown that one can considerably restrict the union operation on conjunctive grammars without changing the generated language. Secondly, certain circuits are investigated whose gates do not compute Boolean values but sets of natural numbers. For these circuits, the equivalence problem is studied, i.\,e.\ the problem of deciding whether two given circuits compute the same set or not. It is shown that, depending on the allowed types of gates, this problem is complete for several different complexity classes and can thus be seen as a parametrized) representative for all those classes.
In the future Internet, the people-centric communication paradigm will be complemented by a ubiquitous communication among people and devices, or even a communication between devices. This comes along with the need for a more flexible, cheap, widely available Internet access. Two types of wireless networks are considered most appropriate for attaining those goals. While wireless sensor networks (WSNs) enhance the Internet’s reach by providing data about the properties of the environment, wireless mesh networks (WMNs) extend the Internet access possibilities beyond the wired backbone. This monograph contains four chapters which present modeling and optimization methods for WSNs and WMNs. Minimizing energy consumptions is the most important goal of WSN optimization and the literature consequently provides countless energy consumption models. The first part of the monograph studies to what extent the used energy consumption model influences the outcome of analytical WSN optimizations. These considerations enable the second contribution, namely overcoming the problems on the way to a standardized energy-efficient WSN communication stack based on IEEE 802.15.4 and ZigBee. For WMNs both problems are of minor interest whereas the network performance has a higher weight. The third part of the work, therefore, presents algorithms for calculating the max-min fair network throughput in WMNs with multiple link rates and Internet gateway. The last contribution of the monograph investigates the impact of the LRA concept which proposes to systematically assign more robust link rates than actually necessary, thereby allowing to exploit the trade-off between spatial reuse and per-link throughput. A systematical study shows that a network-wide slightly more conservative LRA than necessary increases the throughput of a WMN where max-min fairness is guaranteed. It moreover turns out that LRA is suitable for increasing the performance of a contention-based WMN and is a valuable optimization tool.
The field of small satellite formations and constellations attracted growing attention, based on recent advances in small satellite engineering. The utilization of distributed space systems allows the realization of innovative applications and will enable improved temporal and spatial resolution in observation scenarios. On the other side, this new paradigm imposes a variety of research challenges. In this monograph new networking concepts for space missions are presented, using networks of ground stations. The developed approaches combine ground station resources in a coordinated way to achieve more robust and efficient communication links. Within this thesis, the following topics were elaborated to improve the performance in distributed space missions: Appropriate scheduling of contact windows in a distributed ground system is a necessary process to avoid low utilization of ground stations. The theoretical basis for the novel concept of redundant scheduling was elaborated in detail. Additionally to the presented algorithm was a scheduling system implemented, its performance was tested extensively with real world scheduling problems. In the scope of data management, a system was developed which autonomously synchronizes data frames in ground station networks and uses this information to detect and correct transmission errors. The system was validated with hardware in the loop experiments, demonstrating the benefits of the developed approach.
Given a collection of diverging documents about some lost original text, any person interested in the text would try reconstructing it from the diverging documents. Whether it is eclecticism, stemmatics, or copy-text, one is expected to explicitly or indirectly select one of the documents as a starting point or as a base text, which could be emended through comparison with remaining documents, so that a text that could be designated as the original document is generated. Unfortunately the process of giving priority to one of the documents also known as witnesses is a subjective approach. In fact even Cladistics, which could be considered as a computer-based approach of implementing stemmatics, does not present or recommend users to select a certain witness as a starting point for the process of reconstructing the original document. In this study, a computational method using a rule-based Bayesian classifier is used, to assist text scholars in their attempts of reconstructing a non-existing document from some available witnesses. The method developed in this study consists of selecting a base text successively and collating it with remaining documents. Each completed collation cycle stores the selected base text and its closest witness, along with a weighted score of their similarities and differences. At the end of the collation process, a witness selected more often by majority of base texts is considered as the probable base text of the collection. Witnesses’ scores are weighted using a weighting system, based on effects of types of textual modifications on the process of reconstructing original documents. Users have the possibility to select between baseless and base text collation. If a base text is selected, the task is reduced to ranking the witnesses with respect to the base text, otherwise a base text as well as ranking of the witnesses with respect to the base text are computed and displayed on a histogram.
Learning a book in general involves reading it, underlining important words, adding comments, summarizing some passages, and marking up some text or concepts. Once deeper understanding is achieved, one would like to organize and manage her/his knowledge in such a way that, it could be easily remembered and efficiently transmitted to others. In this paper, books organized in terms of chapters consisting of verses, are considered as the source of knowledge to be modeled. The knowledge model consists of verses with their metadata and semantic annotations. The metadata represent the multiple perspectives of knowledge modeling. Verses with their metadata and annotations form a meta-model, which will be published on a web Mashup. The meta-model with linking between its elements constitute a knowledge base. An XML-based annotation system breaking down the learning process into specific tasks, helps constructing the desired meta-model. The system is made up of user interfaces for creating metadata, annotating chapters’ contents according to user selected semantics, and templates for publishing the generated knowledge on the Internet. The proposed software system improves comprehension and retention of knowledge contained in religious texts through modeling and visualization. The system has been applied to the Quran, and the result obtained shows that multiple perspectives of information modeling can be successfully applied to religious texts. It is expected that this short ongoing study would motivate others to engage in devising and offering software systems for cross-religions learning.
Design and Implementation of Architectures for Interactive Textual Documents Collation Systems
(2011)
One of the main purposes of textual documents collation is to identify a base text or closest witness to the base text, by analyzing and interpreting differences also known as types of changes that might exist between those documents. Based on this fact, it is reasonable to argue that, explicit identification of types of changes such as deletions, additions, transpositions, and mutations should be part of the collation process. The identification could be carried out by an interpretation module after alignment has taken place. Unfortunately existing collation software such as CollateX1 and Juxta2’s collation engine do not have interpretation modules. In fact they implement the Gothenburg model [1] for collation process which does not include an interpretation unit. Currently both CollateX and Juxta’s collation engine do not distinguish in their critical apparatus between the types of changes, and do not offer statistics about those changes. This paper presents a model for both integrated and distributed collation processes that improves the Gothenburg model. The model introduces an interpretation component for computing and distinguishing between the types of changes that documents could have undergone. Moreover two architectures implementing the model in order to solve the problem of interactive collation are discussed as well. Each architecture uses CollateX library, and provides on the one hand preprocessing functions for transforming input documents into CollateX input format, and on the other hand a post-processing module for enabling interactive collation. Finally simple algorithms for distinguishing between types of changes, and linking collated source documents with the collation results are also introduced.
The Quran is the holy book of Islam consisting of 6236 verses divided into 114 chapters called suras. Many verses are similar and even identical. Searching for similar texts (e.g verses) could return thousands of verses, that when displayed completely or partly as textual list would make analysis and understanding difficult and confusing. Moreover it would be visually impossible to instantly figure out the overall distribution of the retrieved verses in the Quran. As consequence reading and analyzing the verses would be tedious and unintuitive. In this study a combination of interactive scatter plots and tables has been developed to assist analysis and understanding of the search result. Retrieved verses are clustered by chapters, and a weight is assigned to each cluster according to number of verses it contains, so that users could visually identify most relevant areas, and figure out the places of revelation of the verses. Users visualize the complete result and can select a region of the plot to zoom in, click on a marker to display a table containing verses with English translation side by side.
A Knowledge-based Hybrid Statistical Classifier for Reconstructing the Chronology of the Quran
(2011)
Computationally categorizing Quran’s chapters has been mainly confined to the determination of chapters’ revelation places. However this broad classification is not sufficient to effectively and thoroughly understand and interpret the Quran. The chronology of revelation would not only improve comprehending the philosophy of Islam, but also the easiness of implementing and memorizing its laws and recommendations. This paper attempts estimating possible chapters’ dates of revelation through their lexical frequency profiles. A hybrid statistical classifier consisting of stemming and clustering algorithms for comparing lexical frequency profiles of chapters, and deriving dates of revelation has been developed. The classifier is trained using some chapters with known dates of revelation. Then it classifies chapters with uncertain dates of revelation by computing their proximity to the training ones. The results reported here indicate that the proposed methodology yields usable results in estimating dates of revelation of the Quran’s chapters based on their lexical contents.