A New Approach to Graph Recognition and Applications to Distance-Hereditary Graphs
スポンサーリンク
概要
- 論文の詳細を見る
Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms for such data, we have to propose possible structure models and test if the models are feasible. Hence, it is important to make a compact model for structured data, and enumerate all instances efficiently. There are few graph classes besides trees that can be used for a model. In this paper, we investigate distance-hereditary graphs. This class of graphs consists of isometric graphs and hence contains trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time by using prefix trees. Usually, prefix trees are used to maintain a set of strings. In our algorithm, the prefix trees are used to maintain the neighborhood of vertices, which is a new approach unlike the lexicographically breadth-first search used in other studies. Based on the canonical tree representation, efficient algorithms for the distance-hereditary graphs are proposed, including linear time algorithms for graph recognition and graph isomorphism and an efficient enumeration algorithm. An efficient coding for the tree representation is also presented; it requires ⌈3.59n⌉ bits for a distance-hereditary graph of n vertices and 3n bits for a cograph. The results of coding improve previously known upper bounds (both are 2 ^<O(n log n)>) of the number of distance-hereditary graphs and cographs to 2^<⌈3.59n⌉> and 2^<3n> , respectively.
論文 | ランダム
- Participation in America Revisited--Approach to Socioeconomic Neutrality in Political Participation
- ユニバーサルタウンをめざして--感動を生み、感性を育むまち (特集 こんなまちに住みたい--人がまちをつくり、まちが人をつくる)
- ヨコハマ公園物語, 田中祥夫著, 中央公論新社(中公新書1553), 2000年9月刊, 新書版, 260頁, 780円
- 特集「生物多様性と造園学」にあたって(生物多様性と造園学)
- パ-トナ-シップによるまちづくりの役割分担 (特集 緑のパ-トナ-シップ)