On the Tree Search Problem with Non-uniform Costs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F16%3A00306775" target="_blank" >RIV/68407700:21240/16:00306775 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-662-53174-7_7" target="_blank" >http://dx.doi.org/10.1007/978-3-662-53174-7_7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-662-53174-7_7" target="_blank" >10.1007/978-3-662-53174-7_7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Tree Search Problem with Non-uniform Costs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Tree Search Problem with Non-uniform Costs

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Graph-Theoretic Concepts in Computer Science - 41st International Workshop

ISBN

978-3-662-53173-0

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

13

Strana od-do

90-102

Název nakladatele

Springer

Místo vydání

Munich

Místo konání akce

Munich

Datum konání akce

17. 6. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000389704200007