{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume667","volumeNumber":7391,"name":"Dagstuhl Seminar Proceedings, Volume 7391","dateCreated":"2007-12-18","datePublished":"2007-12-18","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":"#volume667"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article1922","name":"07391 Abstracts Collection \u2013 Probabilistic Methods in the Design and Analysis of Algorithms","abstract":"From 23.09.2007 to 28.09.2007, the Dagstuhl Seminar 07391 \"Probabilistic Methods in the Design and Analysis of Algorithms''was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.\r\nThe seminar brought together leading researchers in probabilistic\r\nmethods to strengthen and foster collaborations among various areas of\r\nTheoretical Computer Science. The interaction between researchers\r\nusing randomization in algorithm design and researchers studying known\r\nalgorithms and heuristics in probabilistic models enhanced the\r\nresearch of both groups in developing new complexity frameworks and in\r\nobtaining new algorithmic results.\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":["Algorithms","Randomization","Probabilistic analysis","Complexity"],"author":[{"@type":"Person","name":"Dietzfelbinger, Martin","givenName":"Martin","familyName":"Dietzfelbinger"},{"@type":"Person","name":"Teng, Shang-Hua","givenName":"Shang-Hua","familyName":"Teng"},{"@type":"Person","name":"Upfal, Eli","givenName":"Eli","familyName":"Upfal"},{"@type":"Person","name":"V\u00f6cking, Berthold","givenName":"Berthold","familyName":"V\u00f6cking"}],"position":1,"pageStart":1,"pageEnd":18,"dateCreated":"2007-12-18","datePublished":"2007-12-18","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Dietzfelbinger, Martin","givenName":"Martin","familyName":"Dietzfelbinger"},{"@type":"Person","name":"Teng, Shang-Hua","givenName":"Shang-Hua","familyName":"Teng"},{"@type":"Person","name":"Upfal, Eli","givenName":"Eli","familyName":"Upfal"},{"@type":"Person","name":"V\u00f6cking, Berthold","givenName":"Berthold","familyName":"V\u00f6cking"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07391.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume667"},{"@type":"ScholarlyArticle","@id":"#article1923","name":"Sampling-based Approximation Algorithms for Multi-stage Stochastic Optimization","abstract":"Stochastic optimization problems provide a means to model uncertainty in the input data where the uncertainty is modeled by a probability distribution over the possible realizations of the data. We consider a broad class of these problems, called {it multi-stage stochastic programming problems with recourse}, where the uncertainty evolves through a series of stages and one take decisions in each stage in response to the new information learned. These problems are often computationally quite difficult with even very specialized (sub)problems being $#P$-complete.\r\n\r\nWe obtain the first fully polynomial randomized approximation scheme (FPRAS) for a broad class of multi-stage stochastic linear programming problems with any constant number of stages, without placing any restrictions on the underlying probability distribution or on the cost structure of the input. For any fixed $k$, for a rich class of $k$-stage stochastic linear programs (LPs), we show that, for any probability distribution, for any $epsilon>0$, one can compute, with high probability, a solution with expected cost at most $(1+e)$ times the optimal expected cost, in time polynomial in the input size, $frac{1}{epsilon}$, and a parameter $lambda$ that is an upper bound on the cost-inflation over successive stages. Moreover, the algorithm analyzed is a simple and intuitive algorithm that is often used in practice, the {it sample average approximation} (SAA) method. In this method, one draws certain samples from the underlying distribution, constructs an approximate distribution from these samples, and solves the stochastic problem given by this approximate distribution. This is the first result establishing that the SAA method yields near-optimal solutions for (a class of) multi-stage programs with a polynomial number of samples.\r\n\r\nAs a corollary of this FPRAS, by adapting a generic rounding technique of Shmoys and Swamy, we also obtain the first approximation algorithms for the analogous class of multi-stage stochastic integer programs, which includes the multi-stage versions of the set cover, vertex cover, multicut on trees, facility location, and multicommodity flow problems.","keywords":["Stochastic optimization","approximation algorithms","randomized algorithms","linear programming"],"author":[{"@type":"Person","name":"Swamy, Chaitanya","givenName":"Chaitanya","familyName":"Swamy"},{"@type":"Person","name":"Shmoys, David","givenName":"David","familyName":"Shmoys"}],"position":2,"pageStart":1,"pageEnd":24,"dateCreated":"2007-12-18","datePublished":"2007-12-18","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Swamy, Chaitanya","givenName":"Chaitanya","familyName":"Swamy"},{"@type":"Person","name":"Shmoys, David","givenName":"David","familyName":"Shmoys"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07391.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume667"},{"@type":"ScholarlyArticle","@id":"#article1924","name":"Smoothed Analysis of Binary Search Trees and Quicksort Under Additive Noise","abstract":"While the height of binary search trees is linear in the worst case, their\r\naverage height is logarithmic. We investigate what happens in between, i.e.,\r\nwhen the randomness is limited, by analyzing the smoothed height of binary\r\nsearch trees: Randomly perturb a given (adversarial) sequence and then take\r\nthe expected height of the binary search tree generated by the resulting\r\nsequence.\r\n\r\nAs perturbation models, we consider partial permutations, where some\r\nelements are randomly permuted, and additive noise, where random numbers\r\nare added to the adversarial sequence. We prove tight bounds for the\r\nsmoothed height of binary search trees under these models. We also obtain\r\ntight bounds for smoothed number of left-to-right maxima. Furthermore, we\r\nexploit the results obtained to get bounds for the smoothed number of\r\ncomparisons that quicksort needs.","keywords":["Smoothed Analysis","Binary Search Trees","Quicksort","Left-to-right Maxima"],"author":[{"@type":"Person","name":"Manthey, Bodo","givenName":"Bodo","familyName":"Manthey"},{"@type":"Person","name":"Tantau, Till","givenName":"Till","familyName":"Tantau"}],"position":3,"pageStart":1,"pageEnd":19,"dateCreated":"2007-12-18","datePublished":"2007-12-18","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Manthey, Bodo","givenName":"Bodo","familyName":"Manthey"},{"@type":"Person","name":"Tantau, Till","givenName":"Till","familyName":"Tantau"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07391.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume667"}]}