On the tree search problem with non-uniform costs

Cicalese, Ferdinando and Keszegh, Balázs and Lidicky, Bernard and Pálvölgyi, Dömötör and Valla, Tomáš (2016) On the tree search problem with non-uniform costs. THEORETICAL COMPUTER SCIENCE, 647. pp. 22-32. ISSN 0304-3975


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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 (logn/logloglogn)-approximation algorithm of Cicalese et al. (2012) [4]. 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 (log n/log log n)-aP proximation 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. (C) 2016 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: WEIGHTED TREES; Edge ranking; Approximation algorithm; Tree search problem; 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; Costs; Computational complexity; Approximation algorithms
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: MTMT SWORD
Date Deposited: 19 Dec 2017 07:21
Last Modified: 19 Dec 2017 07:21

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