### Abstract

Consider a rooted directed acyclic graph G = (V, E) with root r, representing a collection V of web pages connected via a set E of hyperlinks. Each node v is associated with the probability that a user wants to access the node v. The access cost is defined as the expected number of steps required to reach a node from the root r. A bookmark is an additional shortcut from r to a node of G, which may reduce the access cost. The bookmark assignment problem is to find a set of bookmarks that achieves the greatest improvement in the access cost. For the problem, the paper presents a polynomial time approximation algorithm with factor (1 -1/e), and shows that there exists no polynomial time approximation algorithm with a better constant factor than (1-1/e) unless NP ⊆ DTIME(N^{O(log log N})), where N is the size of the inputs.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings |

Pages | 115-124 |

Number of pages | 10 |

Publication status | Published - Dec 1 2007 |

Event | 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007 - Cesky Krumlov, Czech Republic Duration: Aug 26 2007 → Aug 31 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4708 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007 |
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Country | Czech Republic |

City | Cesky Krumlov |

Period | 8/26/07 → 8/31/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings*(pp. 115-124). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4708 LNCS).

**On approximation of bookmark assignments.** / Asahiro, Yuichi; Miyano, Eiji; Murata, Toshihide; Ono, Hirotaka.

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

*Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4708 LNCS, pp. 115-124, 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007, Cesky Krumlov, Czech Republic, 8/26/07.

}

TY - GEN

T1 - On approximation of bookmark assignments

AU - Asahiro, Yuichi

AU - Miyano, Eiji

AU - Murata, Toshihide

AU - Ono, Hirotaka

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Consider a rooted directed acyclic graph G = (V, E) with root r, representing a collection V of web pages connected via a set E of hyperlinks. Each node v is associated with the probability that a user wants to access the node v. The access cost is defined as the expected number of steps required to reach a node from the root r. A bookmark is an additional shortcut from r to a node of G, which may reduce the access cost. The bookmark assignment problem is to find a set of bookmarks that achieves the greatest improvement in the access cost. For the problem, the paper presents a polynomial time approximation algorithm with factor (1 -1/e), and shows that there exists no polynomial time approximation algorithm with a better constant factor than (1-1/e) unless NP ⊆ DTIME(NO(log log N)), where N is the size of the inputs.

AB - Consider a rooted directed acyclic graph G = (V, E) with root r, representing a collection V of web pages connected via a set E of hyperlinks. Each node v is associated with the probability that a user wants to access the node v. The access cost is defined as the expected number of steps required to reach a node from the root r. A bookmark is an additional shortcut from r to a node of G, which may reduce the access cost. The bookmark assignment problem is to find a set of bookmarks that achieves the greatest improvement in the access cost. For the problem, the paper presents a polynomial time approximation algorithm with factor (1 -1/e), and shows that there exists no polynomial time approximation algorithm with a better constant factor than (1-1/e) unless NP ⊆ DTIME(NO(log log N)), where N is the size of the inputs.

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UR - http://www.scopus.com/inward/citedby.url?scp=38049040864&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38049040864

SN - 9783540744559

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 115

EP - 124

BT - Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings

ER -