{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume548","volumeNumber":4421,"name":"Dagstuhl Seminar Proceedings, Volume 4421","dateCreated":"2005-03-24","datePublished":"2005-03-24","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":"#volume548"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article999","name":"04421 Abstracts Collection \u2013 Algebraic Methods in Computational Complexity","abstract":"From 10.10.04 to 15.10.04, the Dagstuhl Seminar 04421 \r\n``Algebraic Methods in Computational Complexity''\r\nwas held in the International Conference and Research Center (IBFI),\r\nSchloss 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":["Computational complexity","algebraic methods","quantum computations","lower bounds"],"author":[{"@type":"Person","name":"Buhrman, Harry","givenName":"Harry","familyName":"Buhrman"},{"@type":"Person","name":"Fortnow, Lance","givenName":"Lance","familyName":"Fortnow"},{"@type":"Person","name":"Thierauf, Thomas","givenName":"Thomas","familyName":"Thierauf"}],"position":1,"pageStart":1,"pageEnd":14,"dateCreated":"2005-04-28","datePublished":"2005-04-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Buhrman, Harry","givenName":"Harry","familyName":"Buhrman"},{"@type":"Person","name":"Fortnow, Lance","givenName":"Lance","familyName":"Fortnow"},{"@type":"Person","name":"Thierauf, Thomas","givenName":"Thomas","familyName":"Thierauf"}],"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"},{"@type":"ScholarlyArticle","@id":"#article1000","name":"Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy","abstract":"This talk surveys some of the work that was \r\ninspired by Wagner's general technique to prove \r\ncompleteness in the levels of the boolean \r\nhierarchy over NP. In particular, we show that \r\nit is DP-complete to decide whether or not a \r\ngiven graph can be colored with exactly four \r\ncolors. DP is the second level of the boolean \r\nhierarchy. This result solves a question raised\r\nby Wagner in his 1987 TCS paper; its proof uses a\r\nclever reduction by Guruswami and Khanna. \r\nSimilar results on various versions of the exact \r\ndomatic number problem are also discussed.\r\nThe result on Exact-Four-Colorability appeared \r\nin IPL, 2003. The results on exact domatic \r\nnumber problems, obtained jointly with Tobias\r\nRiege, are to appear in TOCS.","keywords":["Exact Colorability","exact domatic number","boolean hierarchy completeness"],"author":{"@type":"Person","name":"Rothe, J\u00f6rg","givenName":"J\u00f6rg","familyName":"Rothe"},"position":2,"pageStart":1,"pageEnd":0,"dateCreated":"2005-03-24","datePublished":"2005-03-24","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Rothe, J\u00f6rg","givenName":"J\u00f6rg","familyName":"Rothe"},"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"},{"@type":"ScholarlyArticle","@id":"#article1001","name":"Finding Isolated Cliques by Queries \u2013 An Approach to Fault Diagnosis with Many Faults","abstract":"A well-studied problem in fault diagnosis is to identify the set of all good processors in a given set $\\{p_1,p_2,\\ldots,p_n\\}$\r\nof processors via asking some processors $p_i$ to test whether processor $p_j$ is good or faulty. Mathematically, the set $C$ of the indices of good processors forms an isolated clique in the graph with the edges $E = \\{(i,j):$ if you ask $p_i$\r\nto test $p_j$ then $p_i$ states that ``$p_j$ is good''$\\}$; where $C$ is an isolated clique iff it holds for every $i \\in C$ and $j \\neq i$ that $(i,j) \\in E$ iff $j \\in C$.\r\n\r\nIn the present work, the classical setting of fault diagnosis is modified by no longer requiring that $C$ contains at least $\\frac{n+1}{2}$ of the $n$ nodes of the graph. Instead, one is given a lower bound $a$ on the size of $C$ and the number\r\n$n$ of nodes and one has to find a list of up to $n\/a$ candidates containing all isolated cliques of size $a$ or more where the number of queries whether a given edge is in $E$ is as small as possible.\r\n\r\nIt is shown that the number of queries necessary differs at most by $n$ for the case of directed and undirected graphs. Furthermore,\r\nfor directed graphs the lower bound $n^2\/(2a-2)-3n$ and the upper\r\nbound $2n^2\/a$ are established. For some constant values of $a$, better bounds are given. In the case of parallel queries, the number of rounds is at least $n\/(a-1)-6$ and at most $O(\\log(a)n\/a)$.","keywords":["Isolated Cliques","Query-Complexity","Fault Diagnosis"],"author":[{"@type":"Person","name":"Gasarch, William","givenName":"William","familyName":"Gasarch"},{"@type":"Person","name":"Stephan, Frank","givenName":"Frank","familyName":"Stephan"}],"position":3,"pageStart":1,"pageEnd":16,"dateCreated":"2005-03-24","datePublished":"2005-03-24","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Gasarch, William","givenName":"William","familyName":"Gasarch"},{"@type":"Person","name":"Stephan, Frank","givenName":"Frank","familyName":"Stephan"}],"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"},{"@type":"ScholarlyArticle","@id":"#article1002","name":"Preferences and Domination","abstract":"CP-nets are a succinct formalism for specifying preferences over a multi-featured domain. A CP-net consists of a directed graph, with nodes representing the features of the domain, and edges indicating conditional preferences. \r\nAn instance in the domain is an assignment of values to the features. An instance alpha is preferred to an instance beta if there are a sequence of \"improving flips\" from alpha to beta, where an improving flip changes the value of one feature to a more-preferred value, based on the values of the parents of that feature. We say alpha dominates beta if such a sequence exists.\r\nWe show that recognizing dominance is PSPACE hard for cyclic CP-nets.","keywords":["Preferences","CP-nets","PSPACE-complete","reductions"],"author":{"@type":"Person","name":"Goldsmith, Judy","givenName":"Judy","familyName":"Goldsmith"},"position":4,"pageStart":1,"pageEnd":10,"dateCreated":"2005-03-24","datePublished":"2005-03-24","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Goldsmith, Judy","givenName":"Judy","familyName":"Goldsmith"},"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"},{"@type":"ScholarlyArticle","@id":"#article1003","name":"Randomized QuickSort and the Entropy of the Random Source","abstract":"The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from $n\\log n$ to $n^2$, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution.","keywords":["Randomized Algorithms","QuickSort","Entropy"],"author":[{"@type":"Person","name":"List, Beatrice","givenName":"Beatrice","familyName":"List"},{"@type":"Person","name":"Maucher, Markus","givenName":"Markus","familyName":"Maucher"},{"@type":"Person","name":"Sch\u00f6ning, Uwe","givenName":"Uwe","familyName":"Sch\u00f6ning"},{"@type":"Person","name":"Schuler, Rainer","givenName":"Rainer","familyName":"Schuler"}],"position":5,"pageStart":1,"pageEnd":15,"dateCreated":"2005-03-24","datePublished":"2005-03-24","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"List, Beatrice","givenName":"Beatrice","familyName":"List"},{"@type":"Person","name":"Maucher, Markus","givenName":"Markus","familyName":"Maucher"},{"@type":"Person","name":"Sch\u00f6ning, Uwe","givenName":"Uwe","familyName":"Sch\u00f6ning"},{"@type":"Person","name":"Schuler, Rainer","givenName":"Rainer","familyName":"Schuler"}],"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"},{"@type":"ScholarlyArticle","@id":"#article1004","name":"The communication complexity of the Exact-N Problem revisited","abstract":"If Alice has x, y, Bob has x, z and Carol has y, z can they determine if x+y+z=N? They can if (say) Alice broadcasts x to Bob and Carol; can they do better? Chandra, Furst, and Lipton studied this problem and showed sublinear upper bounds.\r\nThey also had matching (up to an additive constant) lower bounds. We give an exposition of their result with some attention to what happens for particular values of N.","keywords":["Communication Complexity","Exact-N problem","Arithmetic Sequences"],"author":[{"@type":"Person","name":"Gasarch, William","givenName":"William","familyName":"Gasarch"},{"@type":"Person","name":"Glenn, James","givenName":"James","familyName":"Glenn"},{"@type":"Person","name":"Utis, Andre","givenName":"Andre","familyName":"Utis"}],"position":6,"pageStart":1,"pageEnd":14,"dateCreated":"2005-03-24","datePublished":"2005-03-24","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Gasarch, William","givenName":"William","familyName":"Gasarch"},{"@type":"Person","name":"Glenn, James","givenName":"James","familyName":"Glenn"},{"@type":"Person","name":"Utis, Andre","givenName":"Andre","familyName":"Utis"}],"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04421.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume548"}]}