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DOI: 10.4230/LIPIcs.ICALP.2017.84
URN: urn:nbn:de:0030-drops-74507
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7450/
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Dereniowski, Dariusz ; Kosowski, Adrian ; Uznanski, Przemyslaw ; Zou, Mengchuan

Approximation Strategies for Generalized Binary Search in Weighted Trees

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Abstract

We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T\{v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total query cost for a worst-case choice of the target. Designing an optimal strategy for a weighted tree search instance is known to be strongly NP-hard, in contrast to the unweighted variant of the problem which can be solved optimally in linear time. Here, we show that weighted tree search admits a quasi-polynomial time approximation scheme (QPTAS): for any 0 < epsilon < 1, there exists a (1+epsilon)-approximation strategy with a computation time of n^O(log n / epsilon^2). Thus, the problem is not APX-hard, unless NP is contained in DTIME(n^O(log n)). By applying a generic reduction, we obtain as a corollary that the studied problem admits a polynomial-time O(sqrt(log n))-approximation. This improves previous tilde-O(log n)-approximation approaches, where the tilde-O-notation disregards O(poly log log n)-factors.

BibTeX - Entry

@InProceedings{dereniowski_et_al:LIPIcs:2017:7450,
  author =	{Dariusz Dereniowski and Adrian Kosowski and Przemyslaw Uznanski and Mengchuan Zou},
  title =	{{Approximation Strategies for Generalized Binary Search in Weighted Trees}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{84:1--84:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7450},
  URN =		{urn:nbn:de:0030-drops-74507},
  doi =		{10.4230/LIPIcs.ICALP.2017.84},
  annote =	{Keywords: Approximation Algorithm, Adaptive Algorithm, Graph Search, Binary Search, Vertex Ranking, Trees}
}

Keywords: Approximation Algorithm, Adaptive Algorithm, Graph Search, Binary Search, Vertex Ranking, Trees
Seminar: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 06.07.2017


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