Cicalese, F. and Keszegh, Balázs and Lidicky, Bernard and Pálvölgyi, Dömötör and Valla, Tomáš (2016) On the tree search problem with non-uniform costs. In: Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science (9224). Springer, Berlin, pp. 90-102. ISBN 978-3-662-53173-0
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Abstract
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(formula presented)-approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NPhard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2. © Springer-Verlag Berlin Heidelberg 2016.
Item Type: | Book Section |
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Uncontrolled Keywords: | Trees (mathematics); Tree search; Partial order; Ordered structures; Optimal strategies; NP-hard; Novel algorithm; Non-uniform; Associated costs; Parallel processing systems; Optimization; Optimal systems; KNOWLEDGE REPRESENTATION; Graph theory; Costs; Computational complexity; Approximation algorithms; Algorithms |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 03 Jan 2017 11:30 |
Last Modified: | 03 Jan 2017 11:30 |
URI: | http://real.mtak.hu/id/eprint/44387 |
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