Time For Interval Graphs Research Articles

Reconfiguration of Steiner Trees in an Unweighted Graph

We study a reconfiguration problem for Steiner trees in an unweighted graph, which determines whether there exists a sequence of Steiner trees that transforms a given Steiner tree into another one by exchanging a single edge at a time. In this paper, we show that the problem is PSPACE-complete even for split graphs (and hence for chordal graphs), while solvable in linear time for interval graphs.

Computing K-terminal reliability of d-trapezoid graphs

Consider a probabilistic graph in which the edges are perfectly reliable, but vertices may fail with some known probabilities. The K-terminal reliability of this graph is the probability that a given set of vertices K are connected to each other. This reliability problem is known to be #P-complete for general graphs, and it remains #P-complete for chordal graphs and comparability graphs. This work proposes an O(n2d+1)-time algorithm for computing the K-terminal reliability of d-trapezoid graphs. With some modifications, the algorithm is executed in O(n2) time for interval graphs.