Título: | TWO GRAPH OPTIMIZATION PROBLEMS: PIPELINE TRANSPORTATION AND SEARCHING WITH ACCESS COSTS | ||||||||||||||||||||||||||||||||
Autor: |
ARTUR ALVES PESSOA |
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Colaborador(es): |
RUY LUIZ MILIDIU - Orientador EDUARDO SANY LABER - Coorientador |
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Catalogação: | 07/JAN/2004 | Língua(s): | PORTUGUESE - BRAZIL |
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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=4356&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=4356&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.4356 | ||||||||||||||||||||||||||||||||
Resumo: | |||||||||||||||||||||||||||||||||
We consider two combinatorial optimization problems the
pipeline transportation problem (PTD) and the problem of
searching with different access costs (PBC). In PTD, we are
given a directed graph G = (N,A) where each arc corresponds
to a pipeline. We are also given a set of batches, each
batch being initially located at an arc or node and having
a destination node. A subset of these batches are
considered as further batches. Our aim is to find a
sequence of pipeline operations leading all non-further
batches to their corresponding destination nodes. First, we
show that PDT is NP-hard, even for the case where G is
acyclic. Next, we present a polynomial algorithm called
BPA. This algorithm solves PTDS, a variation of PTD, for
general graphs. For acyclic graphs, BPA also minimizes a
general cost function. For the case of makespan
minimization for PTDS, we prove that there is no n1-e -
approximate algorithm for any E]0, unless P = NP, where n
is the instance size. The previous result also holds if G
is both ayclic and planar. In PBC, we are given an ordered
vector with n elements and the corresponding access costs.
Our aim is to find a search strategy that minimizes either
the average cost (PBPC). In both cases, the best known
exact algorithm requires in O(n3) time and O(n2) space. For
PBCM, we present the ratio algorithm, that requires O(n2)
time and O(n3)space. This algorithm always obtains a search
strategy with average cost at most 41n(n+1)/n, assuming the
sum of all access costs to be 1. Furthermore, we introduce
approximation algorithms for both PBCM and PBPC. Both of
them give (2+E+0(1)) - approximate solutions, for any E}0,
in O(n) time and space.
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