Generalization of Binary Search: Searching in Trees and Forest-Like Partial Orders

Speaker(s)

Paweł Parys (joint work with Krzysztof Onak)

Affiliation

Uniwersystet Warszawski

Date

May 30, 2007, 2:15 p.m.

Room

room 5870

Seminar

Seminar Automata Theory

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We extend the binary search technique to searching in trees. We consider two models of queries: questions about vertices and questions about edges. We present a general approach to this sort of problem, and apply it to both cases, achieving algorithms constructing optimal decision trees. In the edge query model the problem is identical to the problem of searching in a special class of tree-like posets stated by Ben-Asher, Farchi and Newman [1]. Our upper bound on computation time, O(n^3), improves the previous best known O(n^4 log n). In the vertex query model we show how to compute an optimal strategy much faster, in O(n) steps. We also present an almost optimal approximation algorithm for another class of tree-like (and forest-like) partial orders.

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