Recognition Algorithm for Probe Interval 2-Trees

Citation data:

British Journal of Mathematics & Computer Science, Vol: 18, Issue: 4, Page: 1-11

Publication Year:
2016
Usage 54
Downloads 35
Abstract Views 19
Repository URL:
https://digitalcommons.wou.edu/fac_pubs/37
DOI:
10.9734/bjmcs/2016/28344
Author(s):
Flesch, Breeann; Nabity, Matthew
Publisher(s):
Sciencedomain International; SCIENCEDOMAIN international
Tags:
Probe interval graph; recognition algorithm; 2-tree; linear-time algorithm; Mathematics
article description
Recognition of probe interval graphs has been studied extensively. Recognition algorithms of probe interval graphs can be broken down into two types of problems: partitioned and non-partitioned. A partitioned recognition algorithm includes the probe and nonprobe partition of the vertices as part of the input, where a non-partitioned algorithm does not include the partition. Partitioned probe interval graphs can be recognized in linear-time in the edges, whereas non-partitioned probe interval graphs can be recognized in polynomial-time. Here we present a non-partitioned recognition algorithm for 2-trees, an extension of trees, that are probe interval graphs. We show that this algorithm runs in O(m) time, where m is the number of edges of a 2-tree. Currently there is no algorithm that performs as well for this problem.