Título: | IMPROVED APPROXIMATIONS FOR THE K-HOTLINK ASSIGNMENT PROBLEM AND FOR BINARY SEARCHING IN TREES | |||||||
Autor: |
MARCO SERPA MOLINARO |
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Colaborador(es): |
EDUARDO SANY LABER - Orientador |
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Catalogação: | 07/JUL/2008 | Língua(s): | ENGLISH - UNITED STATES |
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Tipo: | TEXT | Subtipo: |
THESIS
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Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=11879&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=11879&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.11879 | |||||||
Resumo: | ||||||||
Here we present a study on two optimization problems in
trees: the k-
Hotlink Assignment Problem and the problem of Binary
Searching in Trees.
As a result, we obtain improved approximation algorithms
for both problem.
The k-Hotlink Assignment Problem can be defined as follows.
Let G =
(V,E) be a directed acyclic graph representing a web site,
where nodes
correspond to pages and arcs to hyperlinks. In this
context, hotlinks are
defined as shortcuts (new arcs) added to web pages of G in
order to reduce
the time spent by users to reach their desired information.
Here we consider
the problem where G is a rooted directed tree and the goal
is minimizing the
expected time spent by users by assigning at most k
hotlinks to each node.
For the most studied version of this problem where at most
one hotlink
can be assigned from each node, we prove the existence of
an FPTAS,
improving upon the constant factor algorithm recently
obtained in [Jacobs,
WADS 2007]. In addition, we develop the first constant
factor approximation
algorithm for the most general version where k hotlinks can
be assigned from
each node.
In the second part of this work, we consider the problem of
computing efficient
strategies for searching in trees. As a generalization of
the classical
binary search for ordered lists, suppose one wishes to find
a (unknown) specific
node of a tree by asking queries to its arcs, where each
query indicates
the endpoint closer to the desired node. Given the
likelihood of each node
being the one searched, the objective is to compute a
search strategy that
minimizes the expected number of queries. Practical
applications of this
problem include file system synchronization and software
testing. Here we
present a linear time algorithm which is the first constant
factor approximation
for this problem. This represents a significant improvement
over
previous O(log n)-approximation.
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