On the Tree Search Problem with Non-uniform Costs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F16%3A00306778" target="_blank" >RIV/68407700:21240/16:00306778 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2016.07.019" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2016.07.019</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2016.07.019" target="_blank" >10.1016/j.tcs.2016.07.019</a>
Alternative languages
Result language
angličtina
Original language name
On the Tree Search Problem with Non-uniform Costs
Original language description
Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indices, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial orders and consider the problem of identifying an initially unknown vertex in a tree by asking edge queries: an edge query $e$ returns the component of $T-e$ containing the vertex sought for, while incurring some known cost $c(e)$. The Tree Search Problem with Non-Uniform Cost is the following: given a tree $T$ on $n$ vertices, each edge having an associated cost, construct a strategy that minimizes the total cost of the identification in the worst case. Finding the strategy guaranteeing the minimum possible cost is an NP-complete problem already for input trees of degree 3 or diameter 6. The best known approximation guarantee was an $O(log n/log log log n)$-approximation algorithm of [Cicalese et al. TCS 2012]. We improve upon the above results both from the algorithmic and the computational complexity point of view: We provide a novel algorithm that provides an $O(frac{log n}{log log n})$-approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NP-hard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theoretical Computer Science
ISSN
0304-3975
e-ISSN
1879-2294
Volume of the periodical
647
Issue of the periodical within the volume
September
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
22-32
UT code for WoS article
000383823000002
EID of the result in the Scopus database
2-s2.0-84995691180