New results for the 2-interval pattern problem

We present new results concerning the problem of nding a constrained pattern in a set of 2-intervals. Given a set of n 2-intervals D and a model R describing if two disjoint 2-intervals can be in precedence order (<), be allowed to nest (@) and/or be allowed to cross (G), the problem asks to nd a maximum cardinality subset D ′ ⊆ D such that any two 2-intervals in D ′ agree with R. We improve the time complexity of the best known algorithm for R = {@} by giving an optimal O(n log n) time algorithm. Also, we give a graph-like relaxation for R