An improved g-centroid location algorithm for Ptolemaic graphs
نویسنده
چکیده
We have presented an 2 ( ) O m time algorithm for locating the g-centroid for Ptolemaic graphs, where n is the number of edges and m is the number of vertices of the graph under consideration [6]. If the graph is sparse (i.e. = ( ) m O n ) then the algorithm presented will output the g-centroid in quadratic time. However, for several practical applications, the graph under consideration will be dense (i.e. 2 ( ) m O n ) and the algorithm presented will output gcentroid in 4 ( ) O n time. In this paper, we present an efficient 3 ( ) O n time algorithm to locate the g-centroid for dense Ptolemaic graphs.
منابع مشابه
An efficient g-centroid location algorithm for cographs
In 1998, Pandu Rangan et al. proved that locating the g-centroid for an arbitrary graph is -hard by reducing the problem of finding the maximum clique size of a graph to the g-centroid location problem. They have also given an efficient polynomial time algorithm for locating the g-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present an O(nm) tim...
متن کاملProbe Ptolemaic Graphs
Given a class of graphs, G, a graph G is a probe graph of G if its vertices can be partitioned into two sets, P (the probes) and N (the nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characteri...
متن کاملLaminar Structure of Ptolemaic Graphs and Its Applications
Ptolemaic graphs are graphs that satisfy the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs, and it is a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a laminar structure of cliques, and leads us to a canonical tr...
متن کاملLaminar structure of ptolemaic graphs with applications
Ptolemaic graphs are those satisfying the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. It can also be seen as a natural generalization of block graphs (and hence trees). In this paper, we first state a laminar structure of cliques, which leads to its canonical tree representation. This result is a t...
متن کاملLongest Path Problems on Ptolemaic Graphs
SUMMARY Longest path problem is a problem for finding a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, there are few known graph classes such that the longest path problem can be solved efficiently. Polynomial time algorithms for finding a longest cycle and a longest path in a Ptolemaic graph are pr...
متن کامل