Error Graphs and the Reconstruction of Elements in Groups

Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory which is also based on the consideration of metric balls of vertices, but which is distinct from the traditional packing and covering problems. This problem is motivated by applications in information transmission when redundancy of messages is not sufficient for their exact reconstruction, and applications in computational biology when one wishes to restore an evolutionary process. It can be defined as the reconstruction, or identification, of an unknown vertex in a given graph from a minimal number of vertices (erroneous or distorted patterns) in a metric ball of a given radius r around the unknown vertex. For this problem it is required to find minimum restrictions for such a reconstruction to be possible and also to find efficient reconstruction algorithms under such minimal restrictions. In this paper we define error graphs and investigate their basic properties. A particular class of error graphs occurs when the vertices of the graph are the elements of a group, and when the path metric is determined by a suitable set of group elements. These are the undirected Cayley graphs. Of particular interest is the transposition Cayley graph on the symmetric group which occurs in connection with the analysis of transpositional mutations in molecular biology. We obtain a complete solution of the above problems for the transposition Cayley graph on the symmetric group.Comment: Journal of Combinatorial Theory A 200

Reconstruction of permutations distorted by single transposition errors

The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely reconstructible from 4 distinct permutations at transposition distance at most one from the unknown permutation. The {\it transposition distance} between two permutations is defined as the least number of transpositions needed to transform one into the other. The proposed approach is based on the investigation of structural properties of a corresponding Cayley graph. In the case of at most two transposition errors it is shown that $\frac32(n-2)(n+1)$ erroneous patterns are required in order to reconstruct an unknown permutation. Similar results are obtained for two particular cases when permutations are distorted by given transpositions. These results confirm some bounds for regular graphs which are also presented in this paper.Comment: 5 pages, Report of paper presented at ISIT-200

Application of cover-free codes and combinatorial designs to two-stage testing

AbstractWe study combinatorial and probabilistic properties of cover-free codes and block designs which are useful for their efficient application as the first stage of two-stage group testing procedures. Particular attention is paid to these procedures because of their importance in such applications as monoclonal antibody generation and cDNA library screening

A simple proof of the main inequalities for parameters of codes in polynomial association schemes

Résumé disponible dans le fichier PD

06201 Abstracts Collection -- Combinatorial and Algorithmic Foundations of Pattern and Association Discovery

From 15.05.06 to 20.05.06, the Dagstuhl Seminar 06201 ``Combinatorial and Algorithmic Foundations of Pattern and Association Discovery\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Debugging Inputs

When a program fails to process an input, it need not be the program code that is at fault. It can also be that the input data is faulty, for instance as result of data corruption. To get the data processed, one then has to debug the input data—that is, (1) identify which parts of the input data prevent processing, and (2) recover as much of the (valuable) input data as possible. In this paper, we present a general-purpose algorithm called ddmax that addresses these problems automatically. Through experiments, ddmax maximizes the subset of the input that can still be processed by the program, thus recovering and repairing as much data as possible; the difference between the original failing input and the “maximized” passing input includes all input fragments that could not be processed. To the best of our knowledge, ddmax is the first approach that fixes faults in the input data without requiring program analysis. In our evaluation, ddmax repaired about 69% of input files and recovered about 78% of data within one minute per input

Automated Implementation of Windows-related Security-Configuration Guides

Hardening is the process of configuring IT systems to ensure the security of the systems' components and data they process or store. The complexity of contemporary IT infrastructures, however, renders manual security hardening and maintenance a daunting task. In many organizations, security-configuration guides expressed in the SCAP (Security Content Automation Protocol) are used as a basis for hardening, but these guides by themselves provide no means for automatically implementing the required configurations. In this paper, we propose an approach to automatically extract the relevant information from publicly available security-configuration guides for Windows operating systems using natural language processing. In a second step, the extracted information is verified using the information of available settings stored in the Windows Administrative Template files, in which the majority of Windows configuration settings is defined. We show that our implementation of this approach can extract and implement 83% of the rules without any manual effort and 96% with minimal manual effort. Furthermore, we conduct a study with 12 state-of-the-art guides consisting of 2014 rules with automatic checks and show that our tooling can implement at least 97% of them correctly. We have thus significantly reduced the effort of securing systems based on existing security-configuration guides

Improving OCR of historical newspapers and journals published in Finland

Peer reviewe

Towards Effective Extraction and Linking of Software Mentions from User-Generated Support Tickets

Software support tickets contain short and noisy text from the customers. Software products are often represented by various surface forms and informal abbreviations. Automatically identifying software mentions from support tickets and determining the official names and versions are helpful for many downstream applications, \eg routing the support tickets to the right expert groups for support. In this work, we study the problem ofsoftware product name extraction andlinking from support tickets. We first annotate and analyze sampled tickets to understand the language patterns. Next, we design features using local, contextual, and external information sources, for extraction and linking models. In experiments, we show that linear models with the proposed features are able to deliver better and more consistent results, compared with the state-of-the-art baseline models, even on dataset with sparse labels