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Documents authored by Vigna, Sebastiano

Document
DOI: 10.4230/LIPIcs.FUN.2018.10
Kings, Name Days, Lazy Servants and Magic

Authors: Paolo Boldi and Sebastiano Vigna

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
Once upon a time, a king had a very, very long list of names of his subjects. The king was also a bit obsessed with name days: every day he would ask his servants to look the list for all persons having their name day. Reading every day the whole list was taking an enormous amount of time to the king's servants. One day, the chancellor had a magnificent idea: he wrote a book with instructions. The number of pages in the book was equal to the number of names, but following the instructions one could find all people having their name day by looking at only a few pages - in fact, as many pages as the length of the name - and just glimpsing at the list. Everybody was happy, but in time the king's servants got lazy: when the name was very long they would find excuses to avoid looking at so many pages, and some name days were skipped. Desperate, the king made a call through its reign, and a fat sorceress answered. There was a way to look at much, much fewer pages using an additional magic book. But sometimes, very rarely, it would not work (magic does not always work). The king accepted the offer, and name days parties restarted. Only, once every a few thousand years, the magic book fails, and the assistants have to go by the chancellor book. So the parties start a bit later. But they start anyway.
Cite as

Paolo Boldi and Sebastiano Vigna. Kings, Name Days, Lazy Servants and Magic. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{boldi_et_al:LIPIcs.FUN.2018.10,
  author =	{Boldi, Paolo and Vigna, Sebastiano},
  title =	{{Kings, Name Days, Lazy Servants and Magic}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.10},
  URN =		{urn:nbn:de:0030-drops-88017},
  doi =		{10.4230/LIPIcs.FUN.2018.10},
  annote =	{Keywords: Suffix trees, suffix arrays, z-fast tries, prefix search}
}
Document
DOI: 10.4230/DagSemProc.07071.3
A Deeper Investigation of PageRank as a Function of the Damping Factor

Authors: Paolo Boldi, Massimo Santini, and Sebastiano Vigna

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract
PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor $alpha$ that spreads uniformly part of the rank. The choice of $alpha$ is eminently empirical, and in most cases the original suggestion $alpha=0.85$ by Brin and Page is still used. In this paper, we give a mathematical analysis of PageRank when $alpha$ changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of $alpha$ close to $1$ do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and by proving that the $k$-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree $k$, we show how to obtain an approximation of the derivatives. Finally, we view PageRank as a linear operator acting on the preference vector and show a tight connection between iterated computation and derivation.
Cite as

Paolo Boldi, Massimo Santini, and Sebastiano Vigna. A Deeper Investigation of PageRank as a Function of the Damping Factor. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{boldi_et_al:DagSemProc.07071.3,
  author =	{Boldi, Paolo and Santini, Massimo and Vigna, Sebastiano},
  title =	{{A Deeper Investigation of PageRank as a Function of the Damping Factor}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.3},
  URN =		{urn:nbn:de:0030-drops-10722},
  doi =		{10.4230/DagSemProc.07071.3},
  annote =	{Keywords: PageRank, damping factor, Markov chains}
}
Document
DOI: 10.4230/DagSemProc.07071.15
Stanford Matrix Considered Harmful

Authors: Sebastiano Vigna

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract
I discuss the implications of using small data sets for experiments related to the web graph.
Cite as

Sebastiano Vigna. Stanford Matrix Considered Harmful. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{vigna:DagSemProc.07071.15,
  author =	{Vigna, Sebastiano},
  title =	{{Stanford Matrix Considered Harmful}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.15},
  URN =		{urn:nbn:de:0030-drops-10587},
  doi =		{10.4230/DagSemProc.07071.15},
  annote =	{Keywords: Weg graph, PageRank, HITS}
}
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