### 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 language | English |
---|---|

Pages (from-to) | 1075-1084 |

Number of pages | 10 |

Journal | SIAM Journal on Computing |

Volume | 15 |

Issue number | 4 |

Publication status | Published - Nov 1986 |

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### ASJC Scopus subject areas

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

### Cite this

*SIAM Journal on Computing*,

*15*(4), 1075-1084.

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

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 15, no. 4, pp. 1075-1084.

}

TY - JOUR

T1 - SEARCHING IN TREES, SERIES-PARALLEL AND INTERVAL ORDERS.

AU - Faigle, U.

AU - Lovász, L.

AU - Schrader, R.

AU - Turan, Gy

PY - 1986/11

Y1 - 1986/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022806529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022806529&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022806529

VL - 15

SP - 1075

EP - 1084

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 4

ER -