### Abstract

The Dynamic Finger Conjecture for splay trees states that the cost of m searches on an n-node splay tree is O(m + n + Σ log(|i_{j} - i_{j}-1$/|), where the sum is from i = 1 to m and the jth access is to the i_{j}th item in symmetric order (the i_{0}th item is the item originally at the root of the tree). In other words, the amortized cost of an access is O(1 + log d), where the current access is at distance d from the previous access (distance being measured in terms of the number of items straddled by the two successive accesses); in addition, there is an additive O(n) initialization cost. A bound on the cost is obtained.

Original language | English (US) |
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Title of host publication | Proc 22nd Annu ACM Symp Theory Comput |

Publisher | Publ by ACM |

Pages | 8-17 |

Number of pages | 10 |

ISBN (Print) | 0897913612 |

State | Published - 1990 |

Event | Proceedings of the 22nd Annual ACM Symposium on Theory of Computing - Baltimore, MD, USA Duration: May 14 1990 → May 16 1990 |

### Other

Other | Proceedings of the 22nd Annual ACM Symposium on Theory of Computing |
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City | Baltimore, MD, USA |

Period | 5/14/90 → 5/16/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc 22nd Annu ACM Symp Theory Comput*(pp. 8-17). Publ by ACM.

**On the Dynamic Finger Conjecture for splay trees extended abstract.** / Cole, Richard.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proc 22nd Annu ACM Symp Theory Comput.*Publ by ACM, pp. 8-17, Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 5/14/90.

}

TY - GEN

T1 - On the Dynamic Finger Conjecture for splay trees extended abstract

AU - Cole, Richard

PY - 1990

Y1 - 1990

N2 - The Dynamic Finger Conjecture for splay trees states that the cost of m searches on an n-node splay tree is O(m + n + Σ log(|ij - ij-1$/|), where the sum is from i = 1 to m and the jth access is to the ijth item in symmetric order (the i0th item is the item originally at the root of the tree). In other words, the amortized cost of an access is O(1 + log d), where the current access is at distance d from the previous access (distance being measured in terms of the number of items straddled by the two successive accesses); in addition, there is an additive O(n) initialization cost. A bound on the cost is obtained.

AB - The Dynamic Finger Conjecture for splay trees states that the cost of m searches on an n-node splay tree is O(m + n + Σ log(|ij - ij-1$/|), where the sum is from i = 1 to m and the jth access is to the ijth item in symmetric order (the i0th item is the item originally at the root of the tree). In other words, the amortized cost of an access is O(1 + log d), where the current access is at distance d from the previous access (distance being measured in terms of the number of items straddled by the two successive accesses); in addition, there is an additive O(n) initialization cost. A bound on the cost is obtained.

UR - http://www.scopus.com/inward/record.url?scp=0025137205&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025137205&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897913612

SP - 8

EP - 17

BT - Proc 22nd Annu ACM Symp Theory Comput

PB - Publ by ACM

ER -