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.
British Journal of Mathematics & Computer Science
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Flesch, B., & Nabity, M. (2016). Recognition Algorithm for Probe Interval 2-Trees. British Journal of Mathematics & Computer Science, 18 (4). http://dx.doi.org/10.9734/BJMCS/2016/28344
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