Abstract | ||
---|---|---|
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 23n
, respectively. |
Year | DOI | Venue |
---|---|---|
2009 | 10.1007/s11390-009-9242-3 | Theory and Applications of Models of Computation |
Keywords | Field | DocType |
prefix tree,graph isomorphism,upper bound,linear time,cograph | Discrete mathematics,Combinatorics,Modular decomposition,Trémaux tree,Tree (graph theory),Tree-depth,Computer science,Chordal graph,Cograph,Pathwidth,Split graph | Journal |
Volume | Issue | ISSN |
24 | 3 | 1860-4749 |
Citations | PageRank | References |
8 | 0.53 | 28 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Shin-ichi Nakano | 1 | 246 | 24.40 |
Ryuhei Uehara | 2 | 528 | 75.38 |
Takeaki Uno | 3 | 1319 | 107.99 |