Fully Dynamic Representations of Interval Graphs
نویسنده
چکیده
We present a fully dynamic algorithm that maintains three different representations of an interval graph: a minimal interval model of the graph, the PQ-tree of its maximal cliques, and its modular decomposition. After each vertex or edge modification (insertion or deletion), the algorithm determines whether the new graph is an interval graph in O(n) time, and, in the positive, updates the three representations within the same complexity.
منابع مشابه
Interval Graphs: Canonical Representations in Logspace
We present a logspace algorithm for computing a canonical labeling, in fact a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequence, the isomorphism and automorphism problems for these graph classes are solvable in logspace. ...
متن کاملDAGGER: A Scalable Index for Reachability Queries in Large Dynamic Graphs
With the ubiquity of large-scale graph data in a variety of application domains, querying them effectively is a challenge. In particular, reachability queries are becoming increasingly important, especially for containment, subsumption, and connectivity checks. Whereas many methods have been proposed for static graph reachability, many real-world graphs are constantly evolving, which calls for ...
متن کاملEffective Temporal Graph Layout: A Comparative Study of Animation versus Static Display Methods
Graph drawing algorithms have classically addressed the layout of static graphs. However, the need to draw evolving or dynamic graphs has brought into question many of the assumptions, conventions and layout methods designed to date. For example, social scientists studying evolving social networks have created a demand for visual representations of graphs changing over time. Two common approach...
متن کاملTenacity and some other Parameters of Interval Graphs can be computed in polynomial time
In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...
متن کاملA Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
In this paper we study the problem of recognizing and representing dynamically changing proper interval graphs. The input to the problem consists of a series of modifications to be performed on a graph, where a modification can be a deletion or an addition of a vertex or an edge. The objective is to maintain a representation of the graph as long as it remains a proper interval graph, and to det...
متن کامل