{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume609","volumeNumber":6201,"name":"Dagstuhl Seminar Proceedings, Volume 6201","dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume609"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article1484","name":"06201 Abstracts Collection \u2013 Combinatorial and Algorithmic Foundations of Pattern and Association Discovery","abstract":"From 15.05.06 to 20.05.06, the Dagstuhl Seminar 06201 ``Combinatorial and Algorithmic Foundations of Pattern and Association Discovery'' was held\r\nin the International Conference and Research Center (IBFI), Schloss Dagstuhl.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Data compression","pattern matching","pattern discovery","search","sorting","molecular biology","reconstruction","genome rearrangements"],"author":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Levenshtein, Vladimir I.","givenName":"Vladimir I.","familyName":"Levenshtein"}],"position":1,"pageStart":1,"pageEnd":15,"dateCreated":"2006-11-08","datePublished":"2006-11-08","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Levenshtein, Vladimir I.","givenName":"Vladimir I.","familyName":"Levenshtein"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1485","name":"06201 Executive Summary \u2013 Combinatorial and Algorithmic Foundations of Pattern and Association Discovery","abstract":"The goals of this seminar have been (1) to identify and match\r\nrecently developed methods to specific tasks and data sets in a core of\r\napplication areas; next, based on feedback from the specific applied domain,\r\n(2) to fine tune and personalize those applications, and finally (3) to\r\nidentify and tackle novel combinatorial and algorithmic problems, in some\r\ncases all the way to the development of novel software tools.","keywords":["Data compression","pattern matching","pattern discovery","search","sorting","molecular biology","reconstruction","genome rearrangements"],"author":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Levenshtein, Vladimir I.","givenName":"Vladimir I.","familyName":"Levenshtein"}],"position":2,"pageStart":1,"pageEnd":2,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Levenshtein, Vladimir I.","givenName":"Vladimir I.","familyName":"Levenshtein"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1486","name":"Local Minimax Learning of Approximately Polynomial Functions","abstract":"Suppose we have a number of noisy measurements of an unknown real-valued function $f$ near\r\npoint of interest $mathbf{x}_0 in mathbb{R}^d$. Suppose also that nothing can be assumed\r\nabout the noise distribution, except for zero mean and bounded covariance matrix. We want\r\nto estimate $f$ at $mathbf{x=x}_0$ using a general linear parametric family\r\n$f(mathbf{x};mathbf{a}) = a_0 h_0 (mathbf{x}) ++ a_q h_q (mathbf{x})$, where\r\n$mathbf{a} in mathbb{R}^q$ and $h_i$'s are bounded functions on a neighborhood $B$ of\r\n$mathbf{x}_0$ which contains all points of measurement. Typically, $B$ is a Euclidean ball\r\nor cube in $mathbb{R}^d$ (more generally, a ball in an $l_p$-norm). In the case when the\r\n$h_i$'s are polynomial functions in $x_1,ldots,x_d$ the model is called\r\nlocally-polynomial. In particular, if the $h_i$'s form a basis of the linear space of\r\npolynomials of degree at most two, the model is called locally-quadratic (if the degree is\r\nat most three, the model is locally-cubic, etc.). Often, there is information, which is\r\ncalled context, about the function $f$ (restricted to $B$ ) available, such as that it\r\ntakes values in a known interval, or that it satisfies a Lipschitz condition. The theory of\r\nlocal minimax estimation with context for locally-polynomial models and approximately\r\nlocally polynomial models has been recently initiated by Jones. In the case of local\r\nlinearity and a bound on the change of $f$ on $B$, where $B$ is a ball, the solution for\r\nsquared error loss is in the form of ridge regression, where the ridge parameter is\r\nidentified; hence, minimax justification for ridge regression is given together with\r\nexplicit best error bounds. The analysis of polynomial models of degree above 1 leads to\r\ninteresting and difficult questions in real algebraic geometry and non-linear optimization.\r\n\r\nWe show that in the case when $f$ is a probability function, the optimal (in the minimax\r\nsense) estimator is effectively computable (with any given precision), thanks to Tarski's\r\nelimination principle.","keywords":["Local learning","statistical learning","estimator","minimax","convex optimization","quantifier elimination","semialgebraic","ridge regression","polynomial"],"author":[{"@type":"Person","name":"Jones, Lee","givenName":"Lee","familyName":"Jones"},{"@type":"Person","name":"Rybnikov, Konstantin","givenName":"Konstantin","familyName":"Rybnikov"}],"position":3,"pageStart":1,"pageEnd":12,"dateCreated":"2007-02-13","datePublished":"2007-02-13","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Jones, Lee","givenName":"Lee","familyName":"Jones"},{"@type":"Person","name":"Rybnikov, Konstantin","givenName":"Konstantin","familyName":"Rybnikov"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1487","name":"Non--binary error correcting codes with noiseless feedback, localized errors, or both","abstract":"We investigate non--binary error correcting codes with noiseless feedback, localized errors, or both. It turns out that the Hamming bound is a central concept. For block codes with feedback we present here a coding scheme based on an idea of erasions, which we call the {\\bf rubber method}. It gives an optimal rate for big error correcting fraction $\\tau$ ($>{1\\over q}$) and infinitely many points on the Hamming bound for small $\\tau$.\r\n\r\nWe also consider variable length codes with all lengths bounded from above by $n$ and the end of a word carries the symbol $\\Box$ and is thus recognizable by the decoder. For both, the $\\Box$-model with feedback and the $\\Box$-model with localized errors, the Hamming bound is the exact capacity curve for $\\tau <1\/2.$ Somewhat surprisingly, whereas with feedback the capacity curve coincides with the Hamming bound also for \r\n$1\/2\\leq \\tau \\leq 1$, in this range for localized errors the capacity curve equals 0.\r\n\r\nAlso we give constructions for the models with both, feedback and localized errors.","keywords":["Error-correcting codes","localized errors","feedback","variable length codes"],"author":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Deppe, Christian","givenName":"Christian","familyName":"Deppe"},{"@type":"Person","name":"Lebedev, Vladimir","givenName":"Vladimir","familyName":"Lebedev"}],"position":4,"pageStart":1,"pageEnd":4,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ahlswede, Rudolf","givenName":"Rudolf","familyName":"Ahlswede"},{"@type":"Person","name":"Deppe, Christian","givenName":"Christian","familyName":"Deppe"},{"@type":"Person","name":"Lebedev, Vladimir","givenName":"Vladimir","familyName":"Lebedev"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1488","name":"On the Monotonicity of the String Correction Factor for Words with Mismatches","abstract":"The string correction factor is the term by\r\nwhich the probability of a word $w$ needs to be multiplied in order\r\nto account for character changes or ``errors'' occurring in at most\r\n$k$ arbitrary positions in that word. The behavior of this factor,\r\nas a function of $k$ and of the word length, has implications on the\r\nnumber of candidates that need to be considered and weighted when\r\nlooking for subwords of a sequence that present unusually recurrent\r\nreplicas within some bounded number of mismatches. Specifically, it\r\nis seen that over intervals of mono- or bi-tonicity for the\r\ncorrection factor, only some of the candidates need be considered.\r\nThis mitigates the computation and leads to tables of\r\nover-represented words that are more compact to represent and\r\ninspect. In recent work, expectation and score monotonicity has been\r\nestablished for a number of cases of interest, under {em i.i.d.}\r\nprobabilistic assumptions. The present paper reviews the cases of\r\nbi-tonic behavior for the correction factor, concentrating on the\r\ninstance in which the question is still open.","keywords":["Pattern discovery","Motif","Over-represented word","Monotone score","Correction Factor"],"author":[{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Pizzi, Cinzia","givenName":"Cinzia","familyName":"Pizzi"}],"position":5,"pageStart":1,"pageEnd":9,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Apostolico, Alberto","givenName":"Alberto","familyName":"Apostolico"},{"@type":"Person","name":"Pizzi, Cinzia","givenName":"Cinzia","familyName":"Pizzi"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1489","name":"Sequence prediction for non-stationary processes","abstract":"We address the problem of sequence prediction for nonstationary stochastic processes. In particular, given two measures on the set of one-way infinite sequences over a finite alphabet, consider the question whether one of the measures predicts the other. We find some conditions on local absolute continuity under which prediction is possible.","keywords":["Sequence prediction","probability forecasting","local absolute continuity"],"author":[{"@type":"Person","name":"Ryabko, Daniil","givenName":"Daniil","familyName":"Ryabko"},{"@type":"Person","name":"Hutter, Marcus","givenName":"Marcus","familyName":"Hutter"}],"position":6,"pageStart":1,"pageEnd":12,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ryabko, Daniil","givenName":"Daniil","familyName":"Ryabko"},{"@type":"Person","name":"Hutter, Marcus","givenName":"Marcus","familyName":"Hutter"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1490","name":"Solving Classical String Problems an Compressed Texts","abstract":"How to solve string problems, if instead of input\r\n string we get only program generating it? Is it possible to\r\n solve problems faster than just \"generate text + apply classical\r\n algorithm\"?\r\n\r\n In this paper we consider strings generated by straight-line programs\r\n (SLP). These are programs using only assignment operator. We show\r\n new algorithms for equivalence, pattern matching, finding periods and\r\n covers, computing fingerprint table on SLP-generated strings.\r\n From the other hand, computing the Hamming distance is NP-hard.\r\n\r\n Main corollary is an $O(n2*m)$ algorithm for pattern matching in\r\n LZ-compressed texts.","keywords":["Pattern matching","Compressed text"],"author":{"@type":"Person","name":"Lifshits, Yury","givenName":"Yury","familyName":"Lifshits"},"position":7,"pageStart":1,"pageEnd":10,"dateCreated":"2006-11-10","datePublished":"2006-11-10","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Lifshits, Yury","givenName":"Yury","familyName":"Lifshits"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.7","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1491","name":"Some Results for Identification for Sources and its Extension to Liar Models","abstract":"Let (${cal U}, P$) be a source, where ${cal U} =\r\n{1,2,dots,N}, P = {P_1, P_2, dots, P_N}$, and let ${cal C}\r\n= {c_1,c_2,dots,c_N}$ be a binary prefix code (PC) for this\r\nsource with $||c_u||$ as length of $c_u$. Introduce the random\r\nvariable $U$ with Prob($U=u$) = $p_u$ for $u = 1,2,dots,N$ and\r\nthe random variable $C$ with $C = c_u =\r\n(c_1,c_2,dots,c_{u||c_u||})$ if $U=u$. We use the PC for\r\nnoiseless identification, that is user $u$ wants to know whether\r\nthe source output equals $u$, that is, whether $C$ equals $c_u$ or\r\nnot. The user iteratively checks whether $C$ coincides with $c_u$\r\nin the first, second, etc. letter and stops when the first\r\ndifferent letter occurs or when $C = c_u$. What is the expected\r\nnumber $L_{cal C}(P,u)$ of checkings?\r\n\r\nIn order to calculate this quantity we introduce for the binary\r\ntree $T_{cal C}$, whose leaves are the codewords\r\n$c_1,c_2,dots,c_N$, the sets of leaves ${cal C}_{ik} (1 leq i\r\nleq N; 1 leq k)$, where ${cal C}_{ik} = {c in {cal C}: c$\r\ncoincides with $c_i$ exactly until the $k$'th letter of $c_i}$.\r\nIf $C$ takes a value in ${cal C}_{uk}, 0 leq k leq ||c_u||-1$,\r\nthe answers are $k$ times \"Yes\" and 1 time \"No\". For $C = c_u$ the\r\n$$\r\nL_{cal C}(P,u) = sum_{k=0}^{||c_u||-1}P(C in {cal\r\nC}_{uk})(k+1) + ||c_u||P_u.\r\n$$\r\n\r\nFor code ${cal C}$,~ $L_{cal C}(P) = max L_{cal C}(P,u)$, $1\r\ngeq u geq N$, is the expected number of checkings in the worst\r\ncase and $L(P) = min L_{cal C}(P)$ is this number for the best\r\ncode ${cal C}$.\r\n\r\nLet $P = P^N = {frac{1}{N}, dots, frac{1}{N}}$. We construct\r\na prefix code ${cal C}$ in the following way. In each node\r\n(starting at the root) we split the number of remaining codewords\r\nin proportion as close as possible to $(frac{1}{2},frac{1}{2})$.\r\nIt is known that\r\n$$\r\nlim_{N \r\nightarrow infty} L_{cal C}(P^N) = 2\r\n$$\r\n(Ahlswede, Balkenhol, Kleinewachter, 2003)\r\n\r\nWe know that $L(P) leq 3$ for all $P$ (Ahlswede, Balkenhol, Kleinewachter, 2003). Also, the problem to estimate an universal\r\nconstant $A = sup L(P)$ for general $P = (P_1,dots, P_N)$ was stated (Ahlswede, 2004). We\r\ncompute this constant for uniform distribution and this code\r\n${cal C}$.\r\n$$\r\nsup_N L_{cal C}(P^N) = 2+frac{log_2(N-1)-2}{N}\r\n$$\r\n\r\nAlso, we consider the average number of checkings, if code ${cal\r\nC}$ is used: $ L_{cal C}(P,P) = sum P_u L_{cal C}(P,u)$, for\r\n${u in {cal U}}$. We calculate the exact values of $L_{cal\r\nC}(P^N)$ and $L_{cal C}(P^N,P^N)$ for some $N$.\r\n\r\nOther problem is the extension of identification for sources to\r\nliar models. We obtain a upper bound for the expected number of\r\ncheckings $L_{cal C}(P^N;e)$, where $e$ is the maximum number of\r\nlies.\r\n$$\r\nL_{cal C}(P^N;e) leq M_{cal C}(P^N;e) = (e+1)L_{cal C}(P^N) +\r\ne; ~~ lim_{N \r\nightarrow infty} M_{cal C}(P^N;e) = 3e+2\r\n$$","keywords":["Identification for sources","lies","prefix code"],"author":{"@type":"Person","name":"Varbanov, Zlatko","givenName":"Zlatko","familyName":"Varbanov"},"position":8,"pageStart":1,"pageEnd":4,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Varbanov, Zlatko","givenName":"Zlatko","familyName":"Varbanov"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.8","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1492","name":"Suballowable sequences of permutations","abstract":"We discuss a notion of \"allowable sequence of permutations\" and show a few combinatorial results and geometric applications.","keywords":"Aequences of permutations","author":{"@type":"Person","name":"Asinowski, Andrei","givenName":"Andrei","familyName":"Asinowski"},"position":9,"pageStart":1,"pageEnd":2,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Asinowski, Andrei","givenName":"Andrei","familyName":"Asinowski"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.9","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1493","name":"Subwords in reverse-complement order","abstract":"We examine finite words over an alphabet $Gamma={a,bar{a};b,bar{b}}$ of pairs of letters, where each word $w_1w_2...w_t$ is identical with its {it reverse complement} $bar{w_t}...bar{w_2}bar{w_1}$ (where $bar{bbar{a}}=a,bar{bar{b}}=b$). We seek the smallest $k$ such that every word of length $n,$ composed from $Gamma$, is uniquely determined by the set of its subwords of length up to $k$. Our almost sharp result ($ksim 2n\/3$) is an analogue of a classical result for ``normal'' words.\r\n\r\nThis classical problem originally was posed by M.P. Sch\"utzenberger and I. Simon, and gained a considerable interest for several researchers, foremost by Vladimir Levenshtein.\r\n\r\nOur problem has its roots in bioinformatics.","keywords":["Reverse complement order","Reconstruction of words","Microarray experiments"],"author":[{"@type":"Person","name":"Erd\u00f6s, P\u00e9ter L.","givenName":"P\u00e9ter L.","familyName":"Erd\u00f6s"},{"@type":"Person","name":"Ligeti, P\u00e9ter","givenName":"P\u00e9ter","familyName":"Ligeti"},{"@type":"Person","name":"Sziklai, P\u00e9ter","givenName":"P\u00e9ter","familyName":"Sziklai"},{"@type":"Person","name":"Torney, David C.","givenName":"David C.","familyName":"Torney"}],"position":10,"pageStart":1,"pageEnd":8,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Erd\u00f6s, P\u00e9ter L.","givenName":"P\u00e9ter L.","familyName":"Erd\u00f6s"},{"@type":"Person","name":"Ligeti, P\u00e9ter","givenName":"P\u00e9ter","familyName":"Ligeti"},{"@type":"Person","name":"Sziklai, P\u00e9ter","givenName":"P\u00e9ter","familyName":"Sziklai"},{"@type":"Person","name":"Torney, David C.","givenName":"David C.","familyName":"Torney"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.10","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"},{"@type":"ScholarlyArticle","@id":"#article1494","name":"Vertex reconstruction in Cayley graphs","abstract":"In this report paper we collect recent results on the vertex\r\nreconstruction in Cayley graphs $Cay(G,S)$. The problem is stated as\r\nthe problem of reconstructing a vertex from the minimum number of\r\nits $r$-neighbors that are vertices at distance at most $r$ from the\r\nunknown vertex. The combinatorial properties of Cayley graphs on the\r\nsymmetric group $Sn$ and the signed permutation group $Bn$ with\r\nrespect to this problem are presented. The sets of generators of $S$\r\nare specified by applications in coding theory, computer science,\r\nmolecular biology and physics.","keywords":["Reconstruction problems","Cayley graphs","the symmetric group","the signed permutation group","sorting by reversals","pancake problem"],"author":{"@type":"Person","name":"Konstantinova, Elena","givenName":"Elena","familyName":"Konstantinova"},"position":11,"pageStart":1,"pageEnd":20,"dateCreated":"2006-11-07","datePublished":"2006-11-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Konstantinova, Elena","givenName":"Elena","familyName":"Konstantinova"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06201.11","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume609"}]}