SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS.

U. Faigle, L. Lovász, R. Schrader, Gy Turan

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

N. Linial and M. E. Saks have shown that O(log N) evaluations of an order preserving map, f maps P onto the real numbers, are necessary and sufficient to determine whether alpha is an element of f(P), where N is the number of ideals of P and alpha is a given real number. In this paper, we investigate the problem of how to perform the evaluations so that Linial and Saks' bound is guaranteed to solve the problem for the classes of interval and series-parallel orders and hence, in particular, for rooted trees. We observe that the greedy-type binary search algorithm, which is optimal for chains, already need not be optimal for general rooted trees. We furthermore discuss the computational complexity of the general search problem and obtain results indicating that the general problem might be hard.

Original languageEnglish
Pages (from-to)1075-1084
Number of pages10
JournalSIAM Journal on Computing
Volume15
Issue number4
Publication statusPublished - Nov 1986

Fingerprint

Interval Order
Rooted Trees
Series
Binary search
Computational complexity
Search Problems
Evaluation
Search Algorithm
Computational Complexity
Sufficient
Interval
Necessary

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Faigle, U., Lovász, L., Schrader, R., & Turan, G. (1986). SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS. SIAM Journal on Computing, 15(4), 1075-1084.

SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS. / Faigle, U.; Lovász, L.; Schrader, R.; Turan, Gy.

In: SIAM Journal on Computing, Vol. 15, No. 4, 11.1986, p. 1075-1084.

Research output: Contribution to journalArticle

Faigle, U, Lovász, L, Schrader, R & Turan, G 1986, 'SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS.', SIAM Journal on Computing, vol. 15, no. 4, pp. 1075-1084.
Faigle, U. ; Lovász, L. ; Schrader, R. ; Turan, Gy. / SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS. In: SIAM Journal on Computing. 1986 ; Vol. 15, No. 4. pp. 1075-1084.
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